Question

(x+5)²-(x+5)(x-2)=0
x³+7x²+6x=0

(x+1)²-(2x+3)²=0

Answer 1

1. (x + 5)² - (x + 5)(x - 2) = 0

<=> (x + 5 - x + 2)(x + 5) = 0

<=> 7(x + 5) = 0

<=> x + 5 = 0

<=> x = -5

2. x³ + 7x² + 6x = 0

<=> x³ + x² + 6x² + 6x = 0

<=> x²(x + 1) + 6x(x + 1) = 0

<=> (x² + 6x)(x + 1) = 0

<=> x(x + 6)(x + 1) = 0

<=> \(\left[{}\begin{matrix}x=0\\x+6=0\\x+1=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=0\\x=-6\\x=-1\end{matrix}\right.\)

3. (x + 1)² - (2x + 3)² = 0

<=> (x + 1 + 2x + 3)(x + 1 - 2x - 3) = 0

<=> (3x + 4)(-2 - x) = 0

<=> \(\left[{}\begin{matrix}3x+4=0\\-2-x=0\end{matrix}\right.\)

<=> \(\left[{}\begin{matrix}x=\dfrac{-4}{3}\\x=-2\end{matrix}\right.\)