x^2-2=5x^2-12x-2

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Solution for x^2-2=5x^2-12x-2 equation: 


Simplifying
x2 + -2 = 5x2 + -12x + -2

Reorder the terms:
-2 + x2 = 5x2 + -12x + -2

Reorder the terms:
-2 + x2 = -2 + -12x + 5x2

Add '2' to each side of the equation.
-2 + 2 + x2 = -2 + -12x + 2 + 5x2

Combine like terms: -2 + 2 = 0
0 + x2 = -2 + -12x + 2 + 5x2
x2 = -2 + -12x + 2 + 5x2

Reorder the terms:
x2 = -2 + 2 + -12x + 5x2

Combine like terms: -2 + 2 = 0
x2 = 0 + -12x + 5x2
x2 = -12x + 5x2

Solving
x2 = -12x + 5x2

Solving for variable 'x'.

Reorder the terms:
12x + x2 + -5x2 = -12x + 5x2 + 12x + -5x2

Combine like terms: x2 + -5x2 = -4x2
12x + -4x2 = -12x + 5x2 + 12x + -5x2

Reorder the terms:
12x + -4x2 = -12x + 12x + 5x2 + -5x2

Combine like terms: -12x + 12x = 0
12x + -4x2 = 0 + 5x2 + -5x2
12x + -4x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
12x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + -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 '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0, 3}

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