w^2-3w=27+3w

Solution for w^2-3w=27+3w equation:

Simplifying
w2 + -3w = 27 + 3w

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

Solving
-3w + w2 = 27 + 3w

Solving for variable 'w'.

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

Combine like terms: -3w + -3w = -6w
-27 + -6w + w2 = 27 + 3w + -27 + -3w

Reorder the terms:
-27 + -6w + w2 = 27 + -27 + 3w + -3w

Combine like terms: 27 + -27 = 0
-27 + -6w + w2 = 0 + 3w + -3w
-27 + -6w + w2 = 3w + -3w

Combine like terms: 3w + -3w = 0
-27 + -6w + w2 = 0

Factor a trinomial.
(-3 + -1w)(9 + -1w) = 0

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

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
Subproblem 2
Set the factor '(9 + -1w)' equal to zero and attempt to solve:

Simplifying
9 + -1w = 0

Solving
9 + -1w = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1w = 0 + -9
-1w = 0 + -9

Combine like terms: 0 + -9 = -9
-1w = -9

Divide each side by '-1'.
w = 9

Simplifying
w = 9
Solution
w = {-3, 9}