6(x^2-2)=-x

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

Simplifying
6(x2 + -2) = -1x

Reorder the terms:
6(-2 + x2) = -1x
(-2 * 6 + x2 * 6) = -1x
(-12 + 6x2) = -1x

Solving
-12 + 6x2 = -1x

Solving for variable 'x'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
x = {-1.5, 1.333333333}