7w+w^2=78

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

Simplifying
7w + w2 = 78

Solving
7w + w2 = 78

Solving for variable 'w'.

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

Combine like terms: 78 + -78 = 0
-78 + 7w + w2 = 0

Factor a trinomial.
(-13 + -1w)(6 + -1w) = 0

Subproblem 1
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
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 = {-13, 6}