3(w)(w+9)=270

Solution for 3(w)(w+9)=270 equation:

Simplifying
3(w)(w + 9) = 270

Reorder the terms:
3w(9 + w) = 270
(9 * 3w + w * 3w) = 270
(27w + 3w2) = 270

Solving
27w + 3w2 = 270

Solving for variable 'w'.

Reorder the terms:
-270 + 27w + 3w2 = 270 + -270

Combine like terms: 270 + -270 = 0
-270 + 27w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-90 + 9w + w2) = 0

Factor a trinomial.
3((-15 + -1w)(6 + -1w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-15 + -1w)' equal to zero and attempt to solve:

Simplifying
-15 + -1w = 0

Solving
-15 + -1w = 0

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

Add '15' to each side of the equation.
-15 + 15 + -1w = 0 + 15

Combine like terms: -15 + 15 = 0
0 + -1w = 0 + 15
-1w = 0 + 15

Combine like terms: 0 + 15 = 15
-1w = 15

Divide each side by '-1'.
w = -15

Simplifying
w = -15
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 = {-15, 6}