w^2+8w+12=32

Solution for w^2+8w+12=32 equation:

Simplifying
w2 + 8w + 12 = 32

Reorder the terms:
12 + 8w + w2 = 32

Solving
12 + 8w + w2 = 32

Solving for variable 'w'.

Reorder the terms:
12 + -32 + 8w + w2 = 32 + -32

Combine like terms: 12 + -32 = -20
-20 + 8w + w2 = 32 + -32

Combine like terms: 32 + -32 = 0
-20 + 8w + w2 = 0

Factor a trinomial.
(-10 + -1w)(2 + -1w) = 0

Subproblem 1
Set the factor '(-10 + -1w)' equal to zero and attempt to solve:

Simplifying
-10 + -1w = 0

Solving
-10 + -1w = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1w = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1w = 0 + 10
-1w = 0 + 10

Combine like terms: 0 + 10 = 10
-1w = 10

Divide each side by '-1'.
w = -10

Simplifying
w = -10
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-10, 2}