Solve 3x^2-15xa-x+6=N

$$3 x ^ { 2 } - 15 x a - x + 6 = N$$

Solve for a (complex solution)

$$\left\{\begin{matrix}a=\frac{x}{5}-\frac{N}{15x}-\frac{1}{15}+\frac{2}{5x}\text{, }&x\neq 0\\a\in \mathrm{C}\text{, }&N=6\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides.

$$-15xa-x+6=N-3x^{2}$$

Add x to both sides.

$$-15xa+6=N-3x^{2}+x$$

Subtract 6 from both sides.

$$-15xa=N-3x^{2}+x-6$$

The equation is in standard form.

$$\left(-15x\right)a=-3x^{2}+x+N-6$$

Divide both sides by -15x.

$$\frac{\left(-15x\right)a}{-15x}=\frac{-3x^{2}+x+N-6}{-15x}$$

Dividing by -15x undoes the multiplication by -15x.

$$a=\frac{-3x^{2}+x+N-6}{-15x}$$

Divide N-3x^{2}+x-6 by -15x.

$$a=-\frac{-3x^{2}+x+N-6}{15x}$$

Solve for a

$$\left\{\begin{matrix}a=\frac{x}{5}-\frac{N}{15x}-\frac{1}{15}+\frac{2}{5x}\text{, }&x\neq 0\\a\in \mathrm{R}\text{, }&N=6\text{ and }x=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract 3x^{2} from both sides.

$$-15xa-x+6=N-3x^{2}$$

Add x to both sides.

$$-15xa+6=N-3x^{2}+x$$

Subtract 6 from both sides.

$$-15xa=N-3x^{2}+x-6$$

The equation is in standard form.

$$\left(-15x\right)a=-3x^{2}+x+N-6$$

Divide both sides by -15x.

$$\frac{\left(-15x\right)a}{-15x}=\frac{-3x^{2}+x+N-6}{-15x}$$

Dividing by -15x undoes the multiplication by -15x.

$$a=\frac{-3x^{2}+x+N-6}{-15x}$$

Divide N-3x^{2}+x-6 by -15x.

$$a=-\frac{-3x^{2}+x+N-6}{15x}$$

Solve for N

$$N=3x^{2}-15ax-x+6$$

Solution Steps

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

$$N=3x^{2}-15xa-x+6$$