2w^2+20w+32=0

Solution for 2w^2+20w+32=0 equation:

Simplifying
2w2 + 20w + 32 = 0

Reorder the terms:
32 + 20w + 2w2 = 0

Solving
32 + 20w + 2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 10w + w2) = 0

Factor a trinomial.
2((8 + w)(2 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

Simplifying
w = -2
Solution
w = {-8, -2}