Solve 27x^2-42x+13/B=9x+1+18/B

$$\frac { 27 x ^ { 2 } - 42 x + 13 } { B } = 9 x + 1 + \frac { 18 } { B }$$

Solve for B (complex solution)

$$\left\{\begin{matrix}B=3x-5\text{, }&x\neq \frac{5}{3}\\B\neq 0\text{, }&x=-\frac{1}{9}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$27x^{2}-42x+13=9xB+B+18$$

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

$$9xB+B+18=27x^{2}-42x+13$$

Subtract 18 from both sides.

$$9xB+B=27x^{2}-42x+13-18$$

Subtract 18 from 13 to get -5.

$$9xB+B=27x^{2}-42x-5$$

Combine all terms containing B.

$$\left(9x+1\right)B=27x^{2}-42x-5$$

Divide both sides by 1+9x.

$$\frac{\left(9x+1\right)B}{9x+1}=\frac{\left(3x-5\right)\left(9x+1\right)}{9x+1}$$

Dividing by 1+9x undoes the multiplication by 1+9x.

$$B=\frac{\left(3x-5\right)\left(9x+1\right)}{9x+1}$$

Divide \left(-5+3x\right)\left(1+9x\right) by 1+9x.

$$B=3x-5$$

Variable B cannot be equal to 0.

$$B=3x-5\text{, }B\neq 0$$

Solve for B

$$\left\{\begin{matrix}B=3x-5\text{, }&x\neq -\frac{1}{9}\text{ and }x\neq \frac{5}{3}\\B\neq 0\text{, }&x=-\frac{1}{9}\end{matrix}\right.$$

Steps for Solving Linear Equation

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

$$27x^{2}-42x+13=9xB+B+18$$

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

$$9xB+B+18=27x^{2}-42x+13$$

Subtract 18 from both sides.

$$9xB+B=27x^{2}-42x+13-18$$

Subtract 18 from 13 to get -5.

$$9xB+B=27x^{2}-42x-5$$

Combine all terms containing B.

$$\left(9x+1\right)B=27x^{2}-42x-5$$

Divide both sides by 9x+1.

$$\frac{\left(9x+1\right)B}{9x+1}=\frac{\left(3x-5\right)\left(9x+1\right)}{9x+1}$$

Dividing by 9x+1 undoes the multiplication by 9x+1.

$$B=\frac{\left(3x-5\right)\left(9x+1\right)}{9x+1}$$

Divide \left(-5+3x\right)\left(1+9x\right) by 9x+1.

$$B=3x-5$$

Variable B cannot be equal to 0.

$$B=3x-5\text{, }B\neq 0$$

Solve for x

$$x = -\frac{1}{9} = -0.1111111111111111$$

$$x=\frac{B+5}{3}\text{, }B\neq 0$$