w^2-13w-114=0

Solution for w^2-13w-114=0 equation:

Simplifying
w2 + -13w + -114 = 0

Reorder the terms:
-114 + -13w + w2 = 0

Solving
-114 + -13w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-6 + -1w)(19 + -1w) = 0

Subproblem 1
Set the factor '(-6 + -1w)' equal to zero and attempt to solve:

Simplifying
-6 + -1w = 0

Solving
-6 + -1w = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1w = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1w = 0 + 6
-1w = 0 + 6

Combine like terms: 0 + 6 = 6
-1w = 6

Divide each side by '-1'.
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(19 + -1w)' equal to zero and attempt to solve:

Simplifying
19 + -1w = 0

Solving
19 + -1w = 0

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

Add '-19' to each side of the equation.
19 + -19 + -1w = 0 + -19

Combine like terms: 19 + -19 = 0
0 + -1w = 0 + -19
-1w = 0 + -19

Combine like terms: 0 + -19 = -19
-1w = -19

Divide each side by '-1'.
w = 19

Simplifying
w = 19
Solution
w = {-6, 19}