w^2+5w=66

Solution for w^2+5w=66 equation:

Simplifying
w2 + 5w = 66

Reorder the terms:
5w + w2 = 66

Solving
5w + w2 = 66

Solving for variable 'w'.

Reorder the terms:
-66 + 5w + w2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + 5w + w2 = 0

Factor a trinomial.
(-11 + -1w)(6 + -1w) = 0

Subproblem 1
Set the factor '(-11 + -1w)' equal to zero and attempt to solve:

Simplifying
-11 + -1w = 0

Solving
-11 + -1w = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1w = 0 + 11
-1w = 0 + 11

Combine like terms: 0 + 11 = 11
-1w = 11

Divide each side by '-1'.
w = -11

Simplifying
w = -11
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 = {-11, 6}