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(8 - 5x) (x + 2) + 4(x - 2) (x + 1) + 2(x - 2) (x + 2) = 0
=> (x + 2) [ (8 - 5x) + 4(x + 1) + 2(x - 2)] = 0
=> (x + 2) (8 - 5x + 4x + 4 + 2x - 4) = 0
=> (x + 2) (x + 8) = 0
=> x + 2 = 0 hoặc x + 8 = 0
=> x = -2 hoặc x = -8

(8 - 5x)(x + 2) + 4(x - 2)(x + 1) + 2(x - 2)(x + 2) = 0
=> 8(x + 2) - 5x(x + 2) + 4[x(x + 1) - 2(x + 1)] + 2(x2 - 4) = 0
=> 8x + 16 - 5x2 - 10x + 4(x2 + x - 2x - 2) + 2x2 - 8 = 0
=> 8x + 16 - 5x2 - 10x + 4x2 + 4x - 8x - 8 + 2x2 - 8 = 0
=> (8x - 10x + 4x - 8x) + (16 - 8 - 8) + (-5x2 + 4x2 + 2x2) = 0
=> 0 + x2 = 0
=> x2 = 0 => x = 0
\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)
\(-5x^2-2x+16+4\left(x^2-x-2\right)+2\left(x^2-4\right)=0\)
\(-5x^2-2x+16+4x^2-4x-8+2x^2-8=0\)
\(x^2-6x=0\)
\(x\left(x-6\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x=0\\x-6=0\end{cases}\Rightarrow}\orbr{\begin{cases}x=0\\x=6\end{cases}}\)

\(a.\left(x-2\right)^2-\left(x+3\right)^2-4\left(x+1\right)=5\)
\(\left(x^2-4x+4\right)-\left(x^2+6x+9\right)-4x-4=5\)
\(\left(-4x-6x\right)+\left(4-9\right)-4x-4=5\)
\(-10x-5-4x-4=5\)
\(-14x-9=5\)
\(-14x=14\Rightarrow x=-1\)
\(b.\left(2x-3\right)\left(2x+3\right)-\left(x-1\right)^2-3x\left(x-5\right)=-44\)
\(4x^2-9-\left(x^2-2x+1\right)-\left(3x^2-15x\right)=-44\)
\(4x^2-9-x^2+2x-1-3x^2+15x=-44\)
\(17x-10=-44\)
\(17x=-34\Rightarrow x=-2\)
\(c.\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30\)
\(25x^2+10x+1-\left(25x^2-9\right)=30\)
\(10x+10=30\)
\(10x=20\Rightarrow x=2\)
\(d.\left(x+3\right)^2+\left(x-2\right)\left(x+2\right)-2\left(x-1\right)^2=7\)
\(\left(x^2+6x+9\right)+\left(x^2-4\right)-2\left(x^2-2x+1\right)=7\)
\(2x^2+6x+5-2x^2+4x-2=7\)
\(10x+3=7\)
\(10x=4\Rightarrow x=\frac{4}{10}=\frac25\)
\(f.\left(3x-8\right)^2=0\)
\(3x-8=0\Rightarrow x=\frac83\)
\(e.6\left(x+1\right)^2-2\left(x+1\right)+2\left(x-1\right)\left(x^2+x+1\right)=0\)
\(6\left(x^2+2x+1\right)-2x-2+2\left(x^3-1\right)=0\)
\(6x^2+12x+6-2x-2+2x^3-2=0\)
\(2x^3+6x^2+10x+2=0\)
\(\Rightarrow x\approx-0,23\)

a) (x+2)(x+3)-(x-2)(x+5)=0
\(x^2+3x+2x+6-x^2-5x+2x+10=0\)
\(2x+16=0\)
\(2x=-16\)
\(x=-8\)
Vậy......
b) (8-5x)(x+2)+4(x-2)(x+1)+2(x-2)(x+2)=0
\(8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2+4x-4x-8=0\)
\(-6x+x^2=0\)
\(x\left(-6+x\right)=0\)
=> x=0 hoặc -6+x=0 <=>x=6
Vậy \(x\in\left\{0;6\right\}\)
a) \(\left(x+2\right)\left(x+3\right)-\left(x-2\right)\left(x+5\right)=0\)
\(\Leftrightarrow\left(x+2\right)x+\left(x+2\right).3-\left(x+5\right)x+\left(x+5\right).2=0\)
\(\Leftrightarrow x^2+2x+3x+6-x^2+5x+2x+10=0\)
\(\Leftrightarrow12x+16=0\)
\(\Leftrightarrow12x=-16\)
\(\Leftrightarrow x=\frac{-4}{3}\)
Vậy...
\(\left(8-5x\right)\left(x+2\right)+4\left(x-2\right)\left(x+1\right)+2\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow8x+16-5x^2-10x+4x^2+4x-8x-8+2x^2-8=0\)
\(\Leftrightarrow x^2-6x=0\Leftrightarrow x\left(x-6\right)=0\Leftrightarrow\orbr{\begin{cases}x=0\\x-6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=6\end{cases}}}\)
Vậy S = { 0, 6}