6[x+1][x-1]=13x-12

Solution for 6[x+1][x-1]=13x-12 equation:

Simplifying
6[x + 1][x + -1] = 13x + -12

Reorder the terms:
6[1 + x][x + -1] = 13x + -12

Reorder the terms:
6[1 + x][-1 + x] = 13x + -12

Multiply [1 + x] * [-1 + x]
6[1[-1 + x] + x[-1 + x]] = 13x + -12
6[[-1 * 1 + x * 1] + x[-1 + x]] = 13x + -12
6[[-1 + 1x] + x[-1 + x]] = 13x + -12
6[-1 + 1x + [-1 * x + x * x]] = 13x + -12
6[-1 + 1x + [-1x + x2]] = 13x + -12

Combine like terms: 1x + -1x = 0
6[-1 + 0 + x2] = 13x + -12
6[-1 + x2] = 13x + -12
[-1 * 6 + x2 * 6] = 13x + -12
[-6 + 6x2] = 13x + -12

Reorder the terms:
-6 + 6x2 = -12 + 13x

Solving
-6 + 6x2 = -12 + 13x

Solving for variable 'x'.

Reorder the terms:
-6 + 12 + -13x + 6x2 = -12 + 13x + 12 + -13x

Combine like terms: -6 + 12 = 6
6 + -13x + 6x2 = -12 + 13x + 12 + -13x

Reorder the terms:
6 + -13x + 6x2 = -12 + 12 + 13x + -13x

Combine like terms: -12 + 12 = 0
6 + -13x + 6x2 = 0 + 13x + -13x
6 + -13x + 6x2 = 13x + -13x

Combine like terms: 13x + -13x = 0
6 + -13x + 6x2 = 0

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

Subproblem 1
Set the factor '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 0

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

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

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

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

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
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 = {0.6666666667, 1.5}