2w^2+7w-114=0

Solution for 2w^2+7w-114=0 equation:

Simplifying
2w2 + 7w + -114 = 0

Reorder the terms:
-114 + 7w + 2w2 = 0

Solving
-114 + 7w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-19 + -2w)(6 + -1w) = 0

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

Simplifying
-19 + -2w = 0

Solving
-19 + -2w = 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 + -2w = 0 + 19

Combine like terms: -19 + 19 = 0
0 + -2w = 0 + 19
-2w = 0 + 19

Combine like terms: 0 + 19 = 19
-2w = 19

Divide each side by '-2'.
w = -9.5

Simplifying
w = -9.5
Subproblem 2
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
Solution
w = {-9.5, 6}