x^2-16=2x^2-5x-12

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Solution for x^2-16=2x^2-5x-12 equation: 


Simplifying
x2 + -16 = 2x2 + -5x + -12

Reorder the terms:
-16 + x2 = 2x2 + -5x + -12

Reorder the terms:
-16 + x2 = -12 + -5x + 2x2

Solving
-16 + x2 = -12 + -5x + 2x2

Solving for variable 'x'.

Reorder the terms:
-16 + 12 + 5x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Combine like terms: -16 + 12 = -4
-4 + 5x + x2 + -2x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Combine like terms: x2 + -2x2 = -1x2
-4 + 5x + -1x2 = -12 + -5x + 2x2 + 12 + 5x + -2x2

Reorder the terms:
-4 + 5x + -1x2 = -12 + 12 + -5x + 5x + 2x2 + -2x2

Combine like terms: -12 + 12 = 0
-4 + 5x + -1x2 = 0 + -5x + 5x + 2x2 + -2x2
-4 + 5x + -1x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-4 + 5x + -1x2 = 0 + 2x2 + -2x2
-4 + 5x + -1x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-4 + 5x + -1x2 = 0

Factor a trinomial.
(-4 + x)(1 + -1x) = 0


Subproblem 1
Set the factor '(-4 + x)' equal to zero and attempt to solve:

Simplifying
-4 + x = 0

Solving
-4 + x = 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 + x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + x = 0 + 4
x = 0 + 4

Combine like terms: 0 + 4 = 4
x = 4

Simplifying
x = 4

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
Solution
x = {4, 1}

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