w^2+6w-6=21

Solution for w^2+6w-6=21 equation:

Simplifying
w2 + 6w + -6 = 21

Reorder the terms:
-6 + 6w + w2 = 21

Solving
-6 + 6w + w2 = 21

Solving for variable 'w'.

Reorder the terms:
-6 + -21 + 6w + w2 = 21 + -21

Combine like terms: -6 + -21 = -27
-27 + 6w + w2 = 21 + -21

Combine like terms: 21 + -21 = 0
-27 + 6w + w2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {-9, 3}