Solve 2x(3x-4)=6(x^2-4x-3)

$$2 x ( 3 x - 4 ) = 6 ( x ^ { 2 } - 4 x - 3 )$$

Solve for x

$$x = -\frac{9}{8} = -1\frac{1}{8} = -1.125$$

Steps for Solving Linear Equation

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

$$6x^{2}-8x=6\left(x^{2}-4x-3\right)$$

Use the distributive property to multiply 6 by x^{2}-4x-3.

$$6x^{2}-8x=6x^{2}-24x-18$$

Subtract 6x^{2} from both sides.

$$6x^{2}-8x-6x^{2}=-24x-18$$

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

$$-8x=-24x-18$$

Add 24x to both sides.

$$-8x+24x=-18$$

Combine -8x and 24x to get 16x.

$$16x=-18$$

Divide both sides by 16.

$$x=\frac{-18}{16}$$

Reduce the fraction \frac{-18}{16} to lowest terms by extracting and canceling out 2.

$$x=-\frac{9}{8}$$