0=x^2+4x-117

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Solution for 0=x^2+4x-117 equation: 


Simplifying
0 = x2 + 4x + -117

Reorder the terms:
0 = -117 + 4x + x2

Solving
0 = -117 + 4x + x2

Solving for variable 'x'.

Combine like terms: 0 + 117 = 117
117 + -4x + -1x2 = -117 + 4x + x2 + 117 + -4x + -1x2

Reorder the terms:
117 + -4x + -1x2 = -117 + 117 + 4x + -4x + x2 + -1x2

Combine like terms: -117 + 117 = 0
117 + -4x + -1x2 = 0 + 4x + -4x + x2 + -1x2
117 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
117 + -4x + -1x2 = 0 + x2 + -1x2
117 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
117 + -4x + -1x2 = 0

Factor a trinomial.
(9 + -1x)(13 + x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve:

Simplifying
13 + x = 0

Solving
13 + x = 0

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

Add '-13' to each side of the equation.
13 + -13 + x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + x = 0 + -13
x = 0 + -13

Combine like terms: 0 + -13 = -13
x = -13

Simplifying
x = -13
Solution
x = {9, -13}

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