(w+3)(w)=180

Solution for (w+3)(w)=180 equation:

Simplifying
(w + 3)(w) = 180

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

Reorder the terms for easier multiplication:
w(3 + w) = 180
(3 * w + w * w) = 180
(3w + w2) = 180

Solving
3w + w2 = 180

Solving for variable 'w'.

Reorder the terms:
-180 + 3w + w2 = 180 + -180

Combine like terms: 180 + -180 = 0
-180 + 3w + w2 = 0

Factor a trinomial.
(-15 + -1w)(12 + -1w) = 0

Subproblem 1
Set the factor '(-15 + -1w)' equal to zero and attempt to solve:

Simplifying
-15 + -1w = 0

Solving
-15 + -1w = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1w = 0 + 15
-1w = 0 + 15

Combine like terms: 0 + 15 = 15
-1w = 15

Divide each side by '-1'.
w = -15

Simplifying
w = -15
Subproblem 2
Set the factor '(12 + -1w)' equal to zero and attempt to solve:

Simplifying
12 + -1w = 0

Solving
12 + -1w = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1w = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1w = 0 + -12
-1w = 0 + -12

Combine like terms: 0 + -12 = -12
-1w = -12

Divide each side by '-1'.
w = 12

Simplifying
w = 12
Solution
w = {-15, 12}