2x^2-15x+117+x^2-8x+55=180

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Solution for 2x^2-15x+117+x^2-8x+55=180 equation: 


Simplifying
2x2 + -15x + 117 + x2 + -8x + 55 = 180

Reorder the terms:
117 + 55 + -15x + -8x + 2x2 + x2 = 180

Combine like terms: 117 + 55 = 172
172 + -15x + -8x + 2x2 + x2 = 180

Combine like terms: -15x + -8x = -23x
172 + -23x + 2x2 + x2 = 180

Combine like terms: 2x2 + x2 = 3x2
172 + -23x + 3x2 = 180

Solving
172 + -23x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
172 + -180 + -23x + 3x2 = 180 + -180

Combine like terms: 172 + -180 = -8
-8 + -23x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-8 + -23x + 3x2 = 0

Factor a trinomial.
(-1 + -3x)(8 + -1x) = 0


Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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 = {-0.3333333333, 8}

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