-w^2-7w+78=

Solution for -w^2-7w+78= equation:

Simplifying
-1w2 + -7w + 78 = 0

Reorder the terms:
78 + -7w + -1w2 = 0

Solving
78 + -7w + -1w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(6 + -1w)(13 + w) = 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 '(13 + w)' equal to zero and attempt to solve:

Simplifying
13 + w = 0

Solving
13 + w = 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 + w = 0 + -13

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

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

Simplifying
w = -13
Solution
w = {6, -13}