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\(5x+\frac{2}{6}-8x-\frac{1}{3}=4x+\frac{2}{5}-5\)
<=>\(\frac{30x+10-240x-10}{30}=\frac{120x+12-30}{30}\)
=>-210x=120x-18
<=>-330x=-18
<=>x=\(\frac{330}{18}\)

a. \(3-4x\left(25-2x\right)-8x^2+x-300=0\)
\(\Leftrightarrow3-100x+8x^2-8x^2+x-300=0\)
\(\Leftrightarrow-297-99x=0\)
\(\Leftrightarrow x=3\)
Vậy \(n_0\) của PT là: x=3
b. \(\Leftrightarrow\frac{\left(2-6x\right)}{5}-2+\frac{3x}{10}=7-\frac{3x+3}{4}\)
\(\Leftrightarrow\frac{\left(4-12x\right)}{5}-\frac{20}{10}+\frac{3x}{10}=\frac{\left(28-3x-3\right)}{4}\)
\(\Leftrightarrow\frac{\left(-16-9x\right)}{10}=\frac{\left(25-3x\right)}{4}\)
\(\Leftrightarrow-64-36x=250-30x\)
\(\Leftrightarrow-6x=314\)
\(\Leftrightarrow x=-\frac{157}{3}\)
Vậy -\(n_0\) của PT là: \(x=\frac{-157}{3}\)
c. \(5x+\frac{2}{6}-8x-\frac{1}{3}=4x+\frac{2}{5}-5\)
\(\Leftrightarrow-3x=4x-\frac{23}{5}\)
\(\Leftrightarrow7x=\frac{23}{5}\)
\(\Leftrightarrow x=\frac{23}{35}\)
Vậy \(n_0\) của PT là: \(x=\frac{23}{35}\)
d. \(3x+\frac{2}{3}-3x+\frac{1}{6}=2x+\frac{5}{3}\)
\(\Leftrightarrow\frac{5}{6}=2x+\frac{5}{3}\)
\(\Leftrightarrow x=-\frac{5}{12}\)
Vậy \(n_0\) của Pt là: \(x=-\frac{5}{12}\)

bạn viết rõ đề câu a;b nhé
c, \(2x\left(x-5\right)-\left(x-5\right)=0\Leftrightarrow\left(2x-1\right)\left(x-5\right)=0\Leftrightarrow x=\dfrac{1}{2};x=5\)
d, \(\left(x+3\right)\left(x+3-5+x\right)=0\Leftrightarrow\left(x+3\right)\left(2x-2\right)=0\Leftrightarrow x=-3;x=1\)
e, \(\left(x+2\right)\left(3-4x\right)=\left(x+2\right)^2\Leftrightarrow\left(x+2\right)\left(3-4x-x-2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left(-5x+1\right)=0\Leftrightarrow x=-2;x=\dfrac{1}{5}\)

một đòn bẫy dài một mét .đặt ở đâu để có thể dùng 3600n có thể nâng tảng đá nặng 120kg?

1: \(x^2+3x+2\)
\(=x^2+x+2x+2\)
=x(x+1)+2(x+1)
=(x+1)(x+2)
2: \(x^2+4x+3\)
\(=x^2+x+3x+3\)
=x(x+1)+3(x+1)
=(x+1)(x+3)
3: \(x^2+5x+4\)
\(=x^2+x+4x+4\)
=x(x+1)+4(x+1)
=(x+1)(x+4)
4: \(x^2-4x+3\)
\(=x^2-x-3x+3\)
=x(x-1)-3(x-1)
=(x-1)(x-3)
5: \(x^2-4x+4=x^2-2\cdot x\cdot2+2^2=\left(x-2\right)^2\)
6: \(x^2-5x+4\)
\(=x^2-x-4x+4\)
=x(x-1)-4(x-1)
=(x-1)(x-4)
7: \(x^2-5x+6\)
\(=x^2-2x-3x+6\)
=x(x-2)-3(x-2)
=(x-2)(x-3)
8: \(x^2+6x+5\)
\(=x^2+x+5x+5\)
=x(x+1)+5(x+1)
=(x+1)(x+5)
9: \(x^2-7x+10\)
\(=x^2-2x-5x+10\)
=x(x-2)-5(x-2)
=(x-2)(x-5)
10: \(x^2+8x+12\)
\(=x^2+2x+6x+12\)
=x(x+2)+6(x+2)
=(x+2)(x+6)
11: \(x^2-8x+16=x^2-2\cdot x\cdot4+4^2=\left(x-4\right)^2\)
12: \(x^2+8x+15\)
\(=x^2+3x+5x+15\)
=x(x+3)+5(x+3)
=(x+3)(x+5)
13: \(x^2-8x+7\)
\(=x^2-x-7x+7\)
=x(x-1)-7(x-1)
=(x-1)(x-7)
14: \(x^2+9x+8\)
\(=x^2+x+8x+8\)
=x(x+1)+8(x+1)
=(x+1)(x+8)
15: \(x^2-9x+14\)
\(=x^2-2x-7x+14\)
=x(x-2)-7(x-2)
=(x-2)(x-7)
16: \(x^2+9x+18\)
\(=x^2+3x+6x+18\)
=x(x+3)+6(x+3)
=(x+3)(x+6)
17: \(x^2-9x+20\)
\(=x^2-4x-5x+20\)
=x(x-4)-5(x-4)
=(x-4)(x-5)
18: \(2x^2-3x+1\)
\(=2x^2-2x-x+1\)
=2x(x-1)-(x-1)
=(x-1)(2x-1)
1. \(x^2+3x+2=\left(x+1\right)\left(x+2\right)\)
2. \(x^2+4x+3=\left(x+1\right)\left(x+3\right)\)
3. \(x^2+5x+4=\left(x+1\right)\left(x+4\right)\)
4. \(x^2-4x+3=\left(x-1\right)\left(x-3\right)\)
5. \(x^2-4x+4=\left(x-2\right)^2\)
6. \(x^2-5x+4=\left(x-1\right)\left(x-4\right)\)
7. \(x^2-5x+6=\left(x-2\right)\left(x-3\right)\)
8. \(x^2+6x+5=\left(x+1\right)\left(x+5\right)\)
9. \(x^2-7x+10=\left(x-2\right)\left(x-5\right)\)
10. \(x^2+8x+12=\left(x+2\right)\left(x+6\right)\)
11. \(x^2-8x+16=\left(x-4\right)^2\)
12. \(x^2+8x+15=\left(x+3\right)\left(x+5\right)\)
13. \(x^2-8x+7=\left(x-1\right)\left(x-7\right)\)
14. \(x^2+9x+8=\left(x+1\right)\left(x+8\right)\)
15. \(x^2-9x+14=\left(x-2\right)\left(x-7\right)\)
16. \(x^2+9x+18=\left(x+3\right)\left(x+6\right)\)
17. \(x^2-9x+20=\left(x-4\right)\left(x-5\right)\)
\(18.2x^2-3x+1=2x^2-x-2x+1\)
\(=x\cdot\left(2x-1\right)-\left(2x-1\right)=\left(2x-1\right)\left(x-1\right)\)