360=(6+3w)(w)

Solution for 360=(6+3w)(w) equation:

Simplifying
360 = (6 + 3w)(w)

Reorder the terms for easier multiplication:
360 = w(6 + 3w)
360 = (6 * w + 3w * w)
360 = (6w + 3w2)

Solving
360 = 6w + 3w2

Solving for variable 'w'.

Reorder the terms:
360 + -6w + -3w2 = 6w + -6w + 3w2 + -3w2

Combine like terms: 6w + -6w = 0
360 + -6w + -3w2 = 0 + 3w2 + -3w2
360 + -6w + -3w2 = 3w2 + -3w2

Combine like terms: 3w2 + -3w2 = 0
360 + -6w + -3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(120 + -2w + -1w2) = 0

Factor a trinomial.
3((10 + -1w)(12 + w)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(12 + w)' equal to zero and attempt to solve:

Simplifying
12 + w = 0

Solving
12 + w = 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 + w = 0 + -12

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

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

Simplifying
w = -12
Solution
w = {10, -12}