Solve A=(x-3)(2x+1)+7(2x+1)

$$A = ( x - 3 ) ( 2 x + 1 ) + 7 ( 2 x + 1 )$$

Solve for A

$$A=\left(x+4\right)\left(2x+1\right)$$

Solution Steps

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

$$A=2x^{2}-5x-3+7\left(2x+1\right)$$

Use the distributive property to multiply 7 by 2x+1.

$$A=2x^{2}-5x-3+14x+7$$

Combine -5x and 14x to get 9x.

$$A=2x^{2}+9x-3+7$$

Add -3 and 7 to get 4.

$$A=2x^{2}+9x+4$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{8A+49}-9}{4}$$

$$x=\frac{\sqrt{8A+49}-9}{4}$$

Solve for x

$$x=\frac{-\sqrt{8A+49}-9}{4}$$

$$x=\frac{\sqrt{8A+49}-9}{4}\text{, }A\geq -\frac{49}{8}$$