Đáp án+Giải thích các bước giải:

$a) (x+2)(x+3) - (x-2)(x+5) = 0$

$⇔ x^2 + 5x + 6 - (x^2 + 3x - 10) = 0$

$⇔ x^2 - x^2 + 5x - 3x + 6 - 10=0$
$⇔ 2x - 4 = 0$

$⇔ x = 2$

Vậy $x=2$

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$b) (2x+3)(x-4) + (x-5)(x+2) = (3x-5)(x-4)$

$⇔ (2x-3)(x-4) - (3x-5)(x-4) + (x-5)(x+2) = 0$

$⇔ (x-4)(2x-3-3x+5) + (x-5)(x+2)=0$

$⇔ (x-4)(2-x) + x^2 -3x - 10 = 0$

$⇔ -x^2 +6x - 8 +x^2 - 3x - 10 = 0$
$⇔ 3x - 18 = 0$
$⇔ x=6$

Vậy $x=6$

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$c) (8-5x)(x+2) +4(x-2)(x+1) = 2(2-x)(x+2)$

$⇔ -5x^2 - 2x + 16 + 4(x^2 - x -2) = 2(-x^2 +4)$

$⇔ -5x^2-2x+16 + 4x^2 - 4x - 8 = -2x^2 + 8$

$⇔ -x^2 -6x+8+2x^2-8=0$

$⇔ x^2 - 6x = 0$

$⇔ x(x-6)=0$

$⇔$ \(\left[ \begin{array}{l}x=0\\x=6\end{array} \right.\) 

Vậy $x ∈ ${$0;6$}

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$d) (8x-3)(3x+2) - (4x+7)(x+4) = (2x+1)(5x-1) - 33$

$⇔ 24x^2 + 7x - 6 - (4x^2 +23x + 28) = 10x^2 +3x - 1 - 33$

$⇔ 24x^2 + 7x - 6 - 4x^2 -23x - 28= 10x^2 +3x - 34$

$⇔ 20x^2 -16x - 34 = 10x^2 +3x - 34$

$⇔ 20x^2 -16x - 34 - 10x^2 -3x + 34=0$

$⇔ 10x^2 -19x =0$

$⇔ x(10x - 19) = 0$

$⇔$ \(\left[ \begin{array}{l}x=0\\x=\frac{19}{10}\end{array} \right.\) 

Vậy $x ∈$ {$0;\frac{19}{10}$}