Solve A=(2x+3)(-4x+1)+(2x+3)(8-x)

$$A = ( 2 x + 3 ) ( - 4 x + 1 ) + ( 2 x + 3 ) ( 8 - x )$$

Solve for A

$$A=\left(9-5x\right)\left(2x+3\right)$$

Solution Steps

Use the distributive property to multiply 2x+3 by -4x+1 and combine like terms.

$$A=-8x^{2}-10x+3+\left(2x+3\right)\left(8-x\right)$$

Use the distributive property to multiply 2x+3 by 8-x and combine like terms.

$$A=-8x^{2}-10x+3+13x-2x^{2}+24$$

Combine -10x and 13x to get 3x.

$$A=-8x^{2}+3x+3-2x^{2}+24$$

Combine -8x^{2} and -2x^{2} to get -10x^{2}.

$$A=-10x^{2}+3x+3+24$$

Add 3 and 24 to get 27.

$$A=-10x^{2}+3x+27$$

Solve for x (complex solution)

$$x=\frac{\sqrt{1089-40A}+3}{20}$$

$$x=\frac{-\sqrt{1089-40A}+3}{20}$$

Solve for x

$$x=\frac{\sqrt{1089-40A}+3}{20}$$

$$x=\frac{-\sqrt{1089-40A}+3}{20}\text{, }A\leq \frac{1089}{40}$$