27=6w+w^2

Solution for 27=6w+w^2 equation:

Simplifying
27 = 6w + w2

Solving
27 = 6w + w2

Solving for variable 'w'.

Reorder the terms:
27 + -6w + -1w2 = 6w + -6w + w2 + -1w2

Combine like terms: 6w + -6w = 0
27 + -6w + -1w2 = 0 + w2 + -1w2
27 + -6w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
27 + -6w + -1w2 = 0

Factor a trinomial.
(3 + -1w)(9 + w) = 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 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 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 + w = 0 + -9

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

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

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