x^2-11x-12=-x^2-13x+48

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Solution for x^2-11x-12=-x^2-13x+48 equation: 


Simplifying
x2 + -11x + -12 = -1x2 + -13x + 48

Reorder the terms:
-12 + -11x + x2 = -1x2 + -13x + 48

Reorder the terms:
-12 + -11x + x2 = 48 + -13x + -1x2

Solving
-12 + -11x + x2 = 48 + -13x + -1x2

Solving for variable 'x'.

Reorder the terms:
-12 + -48 + -11x + 13x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2

Combine like terms: -12 + -48 = -60
-60 + -11x + 13x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2

Combine like terms: -11x + 13x = 2x
-60 + 2x + x2 + x2 = 48 + -13x + -1x2 + -48 + 13x + x2

Combine like terms: x2 + x2 = 2x2
-60 + 2x + 2x2 = 48 + -13x + -1x2 + -48 + 13x + x2

Reorder the terms:
-60 + 2x + 2x2 = 48 + -48 + -13x + 13x + -1x2 + x2

Combine like terms: 48 + -48 = 0
-60 + 2x + 2x2 = 0 + -13x + 13x + -1x2 + x2
-60 + 2x + 2x2 = -13x + 13x + -1x2 + x2

Combine like terms: -13x + 13x = 0
-60 + 2x + 2x2 = 0 + -1x2 + x2
-60 + 2x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-60 + 2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-30 + x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(5 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {-6, 5}

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