x^2-12x+40=-x^2+12x-24

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Solution for x^2-12x+40=-x^2+12x-24 equation: 


Simplifying
x2 + -12x + 40 = -1x2 + 12x + -24

Reorder the terms:
40 + -12x + x2 = -1x2 + 12x + -24

Reorder the terms:
40 + -12x + x2 = -24 + 12x + -1x2

Solving
40 + -12x + x2 = -24 + 12x + -1x2

Solving for variable 'x'.

Reorder the terms:
40 + 24 + -12x + -12x + x2 + x2 = -24 + 12x + -1x2 + 24 + -12x + x2

Combine like terms: 40 + 24 = 64
64 + -12x + -12x + x2 + x2 = -24 + 12x + -1x2 + 24 + -12x + x2

Combine like terms: -12x + -12x = -24x
64 + -24x + x2 + x2 = -24 + 12x + -1x2 + 24 + -12x + x2

Combine like terms: x2 + x2 = 2x2
64 + -24x + 2x2 = -24 + 12x + -1x2 + 24 + -12x + x2

Reorder the terms:
64 + -24x + 2x2 = -24 + 24 + 12x + -12x + -1x2 + x2

Combine like terms: -24 + 24 = 0
64 + -24x + 2x2 = 0 + 12x + -12x + -1x2 + x2
64 + -24x + 2x2 = 12x + -12x + -1x2 + x2

Combine like terms: 12x + -12x = 0
64 + -24x + 2x2 = 0 + -1x2 + x2
64 + -24x + 2x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
64 + -24x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -12x + x2) = 0

Factor a trinomial.
2((4 + -1x)(8 + -1x)) = 0

Ignore the factor 2.

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

Simplifying
4 + -1x = 0

Solving
4 + -1x = 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 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {4, 8}

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