(6+w)(w)=216

Solution for (6+w)(w)=216 equation:

Simplifying
(6 + w)(w) = 216

Reorder the terms for easier multiplication:
w(6 + w) = 216
(6 * w + w * w) = 216
(6w + w2) = 216

Solving
6w + w2 = 216

Solving for variable 'w'.

Reorder the terms:
-216 + 6w + w2 = 216 + -216

Combine like terms: 216 + -216 = 0
-216 + 6w + w2 = 0

Factor a trinomial.
(-18 + -1w)(12 + -1w) = 0

Subproblem 1
Set the factor '(-18 + -1w)' equal to zero and attempt to solve:

Simplifying
-18 + -1w = 0

Solving
-18 + -1w = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1w = 0 + 18

Combine like terms: -18 + 18 = 0
0 + -1w = 0 + 18
-1w = 0 + 18

Combine like terms: 0 + 18 = 18
-1w = 18

Divide each side by '-1'.
w = -18

Simplifying
w = -18
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 = {-18, 12}