Solve 6x^2-12/3x-4=2x

$$\frac{ 6 { x }^{ 2 } -12 }{ 3x-4 } =2x$$

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to \frac{4}{3} since division by zero is not defined. Multiply both sides of the equation by 3x-4.

$$6x^{2}-12=2x\left(3x-4\right)$$

Use the distributive property to multiply 2x by 3x-4.

$$6x^{2}-12=6x^{2}-8x$$

Subtract 6x^{2} from both sides.

$$6x^{2}-12-6x^{2}=-8x$$

Combine 6x^{2} and -6x^{2} to get 0.

$$-12=-8x$$

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

$$-8x=-12$$

Divide both sides by -8.

$$x=\frac{-12}{-8}$$

Reduce the fraction \frac{-12}{-8} to lowest terms by extracting and canceling out -4.

$$x=\frac{3}{2}$$