(w+8)(w)=180

Solution for (w+8)(w)=180 equation:

Simplifying
(w + 8)(w) = 180

Reorder the terms:
(8 + w)(w) = 180

Reorder the terms for easier multiplication:
w(8 + w) = 180
(8 * w + w * w) = 180
(8w + w2) = 180

Solving
8w + w2 = 180

Solving for variable 'w'.

Reorder the terms:
-180 + 8w + w2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 8w + w2 = 0

Factor a trinomial.
(-18 + -1w)(10 + -1w) = 0

Subproblem 1
Set the factor '(-18 + -1w)' equal to zero and attempt to solve:

Simplifying
-18 + -1w = 0

Solving
-18 + -1w = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1w = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1w = 0 + 18
-1w = 0 + 18

Combine like terms: 0 + 18 = 18
-1w = 18

Divide each side by '-1'.
w = -18

Simplifying
w = -18
Subproblem 2
Set the factor '(10 + -1w)' equal to zero and attempt to solve:

Simplifying
10 + -1w = 0

Solving
10 + -1w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1w = 0 + -10
-1w = 0 + -10

Combine like terms: 0 + -10 = -10
-1w = -10

Divide each side by '-1'.
w = 10

Simplifying
w = 10
Solution
w = {-18, 10}