72=(6+w)w

Solution for 72=(6+w)w equation:

Simplifying
72 = (6 + w) * w

Reorder the terms for easier multiplication:
72 = w(6 + w)
72 = (6 * w + w * w)
72 = (6w + w2)

Solving
72 = 6w + w2

Solving for variable 'w'.

Reorder the terms:
72 + -6w + -1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
72 + -6w + -1w2 = 0 + w2 + -1w2
72 + -6w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
72 + -6w + -1w2 = 0

Factor a trinomial.
(6 + -1w)(12 + w) = 0

Subproblem 1
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
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 = {6, -12}