Solve 6x(x-2)-(x-2)(3x-1)=3x^2-8

$$6 x ( x - 2 ) - ( x - 2 ) ( 3 x - 1 ) = 3 x ^ { 2 } - 8$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 6x by x-2.

$$6x^{2}-12x-\left(x-2\right)\left(3x-1\right)=3x^{2}-8$$

Use the distributive property to multiply x-2 by 3x-1 and combine like terms.

$$6x^{2}-12x-\left(3x^{2}-7x+2\right)=3x^{2}-8$$

To find the opposite of 3x^{2}-7x+2, find the opposite of each term.

$$6x^{2}-12x-3x^{2}+7x-2=3x^{2}-8$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$3x^{2}-12x+7x-2=3x^{2}-8$$

Combine -12x and 7x to get -5x.

$$3x^{2}-5x-2=3x^{2}-8$$

Subtract 3x^{2} from both sides.

$$3x^{2}-5x-2-3x^{2}=-8$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-5x-2=-8$$

Add 2 to both sides.

$$-5x=-8+2$$

Add -8 and 2 to get -6.

$$-5x=-6$$

Divide both sides by -5.

$$x=\frac{-6}{-5}$$

Fraction \frac{-6}{-5} can be simplified to \frac{6}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{6}{5}$$