Solve A=left(3x+2right)^2-2xleft(2x-3right)

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

Solve for A

$$A=5x^{2}+18x+4$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+2\right)^{2}.

$$A=9x^{2}+12x+4-2x\left(2x-3\right)$$

Use the distributive property to multiply -2x by 2x-3.

$$A=9x^{2}+12x+4-4x^{2}+6x$$

Combine 9x^{2} and -4x^{2} to get 5x^{2}.

$$A=5x^{2}+12x+4+6x$$

Combine 12x and 6x to get 18x.

$$A=5x^{2}+18x+4$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{5A+61}-9}{5}$$

$$x=\frac{\sqrt{5A+61}-9}{5}$$

Solve for x

$$x=\frac{-\sqrt{5A+61}-9}{5}$$

$$x=\frac{\sqrt{5A+61}-9}{5}\text{, }A\geq -\frac{61}{5}$$