w^2+w-182=0

Solution for w^2+w-182=0 equation:

Simplifying
w2 + w + -182 = 0

Reorder the terms:
-182 + w + w2 = 0

Solving
-182 + w + w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-14 + -1w)(13 + -1w) = 0

Subproblem 1
Set the factor '(-14 + -1w)' equal to zero and attempt to solve:

Simplifying
-14 + -1w = 0

Solving
-14 + -1w = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1w = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1w = 0 + 14
-1w = 0 + 14

Combine like terms: 0 + 14 = 14
-1w = 14

Divide each side by '-1'.
w = -14

Simplifying
w = -14
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 = {-14, 13}