w^2-4w-117=0

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Solution for w^2-4w-117=0 equation: 


Simplifying
w2 + -4w + -117 = 0

Reorder the terms:
-117 + -4w + w2 = 0

Solving
-117 + -4w + w2 = 0

Solving for variable 'w'.

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


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

Simplifying
-9 + -1w = 0

Solving
-9 + -1w = 0

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

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

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

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

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

Simplifying
w = -9

Subproblem 2
Set the factor '(13 + -1w)' equal to zero and attempt to solve:

Simplifying
13 + -1w = 0

Solving
13 + -1w = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1w = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1w = 0 + -13
-1w = 0 + -13

Combine like terms: 0 + -13 = -13
-1w = -13

Divide each side by '-1'.
w = 13

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

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