Solve y=[(2x-1)(x+3)]^2

$$y = [ ( 2 x - 1 ) ( x + 3 ) ] ^ { 2 }$$

Solve for y

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

Solution Steps

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

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

Square 2x^{2}+5x-3.

$$y=4x^{4}+20x^{3}+13x^{2}-30x+9$$

Solve for x (complex solution)

$$x=\frac{-\sqrt{8\sqrt{y}+49}-5}{4}$$

$$x=\frac{\sqrt{8\sqrt{y}+49}-5}{4}$$

$$x=\frac{\sqrt{-8\sqrt{y}+49}-5}{4}$$

$$x=\frac{-\sqrt{-8\sqrt{y}+49}-5}{4}$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-\sqrt{8\sqrt{y}+49}-5}{4}\text{; }x=\frac{\sqrt{8\sqrt{y}+49}-5}{4}\text{, }&y\geq 0\\x=\frac{-\sqrt{-8\sqrt{y}+49}-5}{4}\text{; }x=\frac{\sqrt{-8\sqrt{y}+49}-5}{4}\text{, }&y\geq 0\text{ and }y\leq \frac{2401}{64}\end{matrix}\right.$$