Solve A=(x+7)(x-4)+(-4+x)(x+2)

$$A = ( x + 7 ) ( x - 4 ) + ( - 4 + x ) ( x + 2 )$$

Solve for A

$$A=\left(x-4\right)\left(2x+9\right)$$

Solution Steps

Use the distributive property to multiply x+7 by x-4 and combine like terms.

$$A=x^{2}+3x-28+\left(-4+x\right)\left(x+2\right)$$

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

$$A=x^{2}+3x-28-2x-8+x^{2}$$

Combine 3x and -2x to get x.

$$A=x^{2}+x-28-8+x^{2}$$

Subtract 8 from -28 to get -36.

$$A=x^{2}+x-36+x^{2}$$

Combine x^{2} and x^{2} to get 2x^{2}.

$$A=2x^{2}+x-36$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{8A+289}-1}{4}$$

$$x=\frac{\sqrt{8A+289}-1}{4}$$

Solve for x

$$x=\frac{-\sqrt{8A+289}-1}{4}$$

$$x=\frac{\sqrt{8A+289}-1}{4}\text{, }A\geq -\frac{289}{8}$$