x^2-5x+3x+117=180

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Solution for x^2-5x+3x+117=180 equation: 


Simplifying
x2 + -5x + 3x + 117 = 180

Reorder the terms:
117 + -5x + 3x + x2 = 180

Combine like terms: -5x + 3x = -2x
117 + -2x + x2 = 180

Solving
117 + -2x + x2 = 180

Solving for variable 'x'.

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

Combine like terms: 117 + -180 = -63
-63 + -2x + x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-63 + -2x + x2 = 0

Factor a trinomial.
(-7 + -1x)(9 + -1x) = 0


Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve:

Simplifying
-7 + -1x = 0

Solving
-7 + -1x = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1x = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1x = 0 + 7
-1x = 0 + 7

Combine like terms: 0 + 7 = 7
-1x = 7

Divide each side by '-1'.
x = -7

Simplifying
x = -7

Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve:

Simplifying
9 + -1x = 0

Solving
9 + -1x = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1x = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1x = 0 + -9
-1x = 0 + -9

Combine like terms: 0 + -9 = -9
-1x = -9

Divide each side by '-1'.
x = 9

Simplifying
x = 9
Solution
x = {-7, 9}

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