w(6+w)=72

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

Simplifying
w(6 + w) = 72
(6 * w + w * w) = 72
(6w + w2) = 72

Solving
6w + w2 = 72

Solving for variable 'w'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-12, 6}