Solve 3x^2+1^2x-2=9n

$$3 x ^ { 2 } + 1 ^ { 2 } x - 2 = 9 n$$

Solve for n

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

Steps for Solving Linear Equation

Calculate 1 to the power of 2 and get 1.

$$3x^{2}+1x-2=9n$$

Swap sides so that all variable terms are on the left hand side.

$$9n=3x^{2}+1x-2$$

Reorder the terms.

$$9n=3x^{2}+x-2$$

Divide both sides by 9.

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

Dividing by 9 undoes the multiplication by 9.

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

Solve for x (complex solution)

$$x=\frac{\sqrt{108n+25}-1}{6}$$

$$x=\frac{-\sqrt{108n+25}-1}{6}$$

Solve for x

$$x=\frac{\sqrt{108n+25}-1}{6}$$

$$x=\frac{-\sqrt{108n+25}-1}{6}\text{, }n\geq -\frac{25}{108}$$