6(x^2-2)=x

Solution for 6(x^2-2)=x equation:

Simplifying
6(x2 + -2) = x

Reorder the terms:
6(-2 + x2) = x
(-2 * 6 + x2 * 6) = x
(-12 + 6x2) = x

Solving
-12 + 6x2 = x

Solving for variable 'x'.

Reorder the terms:
-12 + -1x + 6x2 = x + -1x

Combine like terms: x + -1x = 0
-12 + -1x + 6x2 = 0

Factor a trinomial.
(-4 + -3x)(3 + -2x) = 0

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-1.333333333, 1.5}