480=(14+w)(w)

Solution for 480=(14+w)(w) equation:

Simplifying
480 = (14 + w)(w)

Reorder the terms for easier multiplication:
480 = w(14 + w)
480 = (14 * w + w * w)
480 = (14w + w2)

Solving
480 = 14w + w2

Solving for variable 'w'.

Reorder the terms:
480 + -14w + -1w2 = 14w + -14w + w2 + -1w2

Combine like terms: 14w + -14w = 0
480 + -14w + -1w2 = 0 + w2 + -1w2
480 + -14w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
480 + -14w + -1w2 = 0

Factor a trinomial.
(16 + -1w)(30 + w) = 0

Subproblem 1
Set the factor '(16 + -1w)' equal to zero and attempt to solve:

Simplifying
16 + -1w = 0

Solving
16 + -1w = 0

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

Add '-16' to each side of the equation.
16 + -16 + -1w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -1w = 0 + -16
-1w = 0 + -16

Combine like terms: 0 + -16 = -16
-1w = -16

Divide each side by '-1'.
w = 16

Simplifying
w = 16
Subproblem 2
Set the factor '(30 + w)' equal to zero and attempt to solve:

Simplifying
30 + w = 0

Solving
30 + w = 0

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

Add '-30' to each side of the equation.
30 + -30 + w = 0 + -30

Combine like terms: 30 + -30 = 0
0 + w = 0 + -30
w = 0 + -30

Combine like terms: 0 + -30 = -30
w = -30

Simplifying
w = -30
Solution
w = {16, -30}