Solve y=(9x^2-2)(3x+1)/u

$$y = \frac { ( 9 x ^ { 2 } - 2 ) ( 3 x + 1 ) } { u }$$

Solve for u

$$\left\{\begin{matrix}u=\frac{\left(3x+1\right)\left(9x^{2}-2\right)}{y}\text{, }&x\neq -\frac{1}{3}\text{ and }y\neq 0\text{ and }|x|\neq \frac{\sqrt{2}}{3}\\u\neq 0\text{, }&\left(x=-\frac{1}{3}\text{ or }|x|=\frac{\sqrt{2}}{3}\right)\text{ and }y=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Variable u cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by u.

$$yu=\left(9x^{2}-2\right)\left(3x+1\right)$$

Use the distributive property to multiply 9x^{2}-2 by 3x+1.

$$yu=27x^{3}+9x^{2}-6x-2$$

Divide both sides by y.

$$\frac{yu}{y}=\frac{\left(3x+1\right)\left(9x^{2}-2\right)}{y}$$

Dividing by y undoes the multiplication by y.

$$u=\frac{\left(3x+1\right)\left(9x^{2}-2\right)}{y}$$

Variable u cannot be equal to 0.

$$u=\frac{\left(3x+1\right)\left(9x^{2}-2\right)}{y}\text{, }u\neq 0$$