x^2-6=5x^2-8x-6

Solution for x^2-6=5x^2-8x-6 equation:

Simplifying
x2 + -6 = 5x2 + -8x + -6

Reorder the terms:
-6 + x2 = 5x2 + -8x + -6

Reorder the terms:
-6 + x2 = -6 + -8x + 5x2

Add '6' to each side of the equation.
-6 + 6 + x2 = -6 + -8x + 6 + 5x2

Combine like terms: -6 + 6 = 0
0 + x2 = -6 + -8x + 6 + 5x2
x2 = -6 + -8x + 6 + 5x2

Reorder the terms:
x2 = -6 + 6 + -8x + 5x2

Combine like terms: -6 + 6 = 0
x2 = 0 + -8x + 5x2
x2 = -8x + 5x2

Solving
x2 = -8x + 5x2

Solving for variable 'x'.

Reorder the terms:
8x + x2 + -5x2 = -8x + 5x2 + 8x + -5x2

Combine like terms: x2 + -5x2 = -4x2
8x + -4x2 = -8x + 5x2 + 8x + -5x2

Reorder the terms:
8x + -4x2 = -8x + 8x + 5x2 + -5x2

Combine like terms: -8x + 8x = 0
8x + -4x2 = 0 + 5x2 + -5x2
8x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
8x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(2 + -1x) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}