Solve y=2x^2(3x^3-7x)/x

$$y = \frac { 2 x ^ { 2 } ( 3 x ^ { 3 } - 7 x ) } { x }$$

Solve for y

$$y=6x^{4}-14x^{2}$$

$$x\neq 0$$

Solution Steps

Cancel out x in both numerator and denominator.

$$y=2x\left(3x^{3}-7x\right)$$

Use the distributive property to multiply 2x by 3x^{3}-7x.

$$y=6x^{4}-14x^{2}$$

Solve for x (complex solution)

$$\left\{\begin{matrix}\\x=-\frac{\sqrt{6\sqrt{6y+49}+42}}{6}\text{; }x=\frac{\sqrt{6\sqrt{6y+49}+42}}{6}\text{, }&\text{unconditionally}\\x=-\frac{\sqrt{-6\sqrt{6y+49}+42}}{6}\text{; }x=\frac{\sqrt{-6\sqrt{6y+49}+42}}{6}\text{, }&y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{\sqrt{-6\sqrt{6y+49}+42}}{6}\text{; }x=-\frac{\sqrt{-6\sqrt{6y+49}+42}}{6}\text{, }&y\geq -\frac{49}{6}\text{ and }y<0\\x=\frac{\sqrt{6\sqrt{6y+49}+42}}{6}\text{; }x=-\frac{\sqrt{6\sqrt{6y+49}+42}}{6}\text{, }&y\geq -\frac{49}{6}\end{matrix}\right.$$