(2(x^2-6))=(13x+12)

Solution for (2(x^2-6))=(13x+12) equation:

Simplifying
(2(x2 + -6)) = (13x + 12)

Reorder the terms:
(2(-6 + x2)) = (13x + 12)
((-6 * 2 + x2 * 2)) = (13x + 12)
((-12 + 2x2)) = (13x + 12)
(-12 + 2x2) = (13x + 12)

Remove parenthesis around (-12 + 2x2)
-12 + 2x2 = (13x + 12)

Reorder the terms:
-12 + 2x2 = (12 + 13x)

Remove parenthesis around (12 + 13x)
-12 + 2x2 = 12 + 13x

Solving
-12 + 2x2 = 12 + 13x

Solving for variable 'x'.

Reorder the terms:
-12 + -12 + -13x + 2x2 = 12 + 13x + -12 + -13x

Combine like terms: -12 + -12 = -24
-24 + -13x + 2x2 = 12 + 13x + -12 + -13x

Reorder the terms:
-24 + -13x + 2x2 = 12 + -12 + 13x + -13x

Combine like terms: 12 + -12 = 0
-24 + -13x + 2x2 = 0 + 13x + -13x
-24 + -13x + 2x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
-24 + -13x + 2x2 = 0

Factor a trinomial.
(-3 + -2x)(8 + -1x) = 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 '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {-1.5, 8}