Solve -(2x+2)^2=(x-4)(x+2)(-4)

$$- ( 2 x + 2 ) ^ { 2 } = ( x - 4 ) ( x + 2 ) ( - 4 )$$

Solve for x

$$x = -\frac{9}{4} = -2\frac{1}{4} = -2.25$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2x+2\right)^{2}.

$$-\left(4x^{2}+8x+4\right)=\left(x-4\right)\left(x+2\right)\left(-4\right)$$

To find the opposite of 4x^{2}+8x+4, find the opposite of each term.

$$-4x^{2}-8x-4=\left(x-4\right)\left(x+2\right)\left(-4\right)$$

Use the distributive property to multiply x-4 by x+2 and combine like terms.

$$-4x^{2}-8x-4=\left(x^{2}-2x-8\right)\left(-4\right)$$

Use the distributive property to multiply x^{2}-2x-8 by -4.

$$-4x^{2}-8x-4=-4x^{2}+8x+32$$

Add 4x^{2} to both sides.

$$-4x^{2}-8x-4+4x^{2}=8x+32$$

Combine -4x^{2} and 4x^{2} to get 0.

$$-8x-4=8x+32$$

Subtract 8x from both sides.

$$-8x-4-8x=32$$

Combine -8x and -8x to get -16x.

$$-16x-4=32$$

Add 4 to both sides.

$$-16x=32+4$$

Add 32 and 4 to get 36.

$$-16x=36$$

Divide both sides by -16.

$$x=\frac{36}{-16}$$

Reduce the fraction \frac{36}{-16} to lowest terms by extracting and canceling out 4.

$$x=-\frac{9}{4}$$