2w^2-16w=-32

Solution for 2w^2-16w=-32 equation:

Simplifying
2w2 + -16w = -32

Reorder the terms:
-16w + 2w2 = -32

Solving
-16w + 2w2 = -32

Solving for variable 'w'.

Reorder the terms:
32 + -16w + 2w2 = -32 + 32

Combine like terms: -32 + 32 = 0
32 + -16w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + -8w + w2) = 0

Factor a trinomial.
2((4 + -1w)(4 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Subproblem 2
Set the factor '(4 + -1w)' equal to zero and attempt to solve:

Simplifying
4 + -1w = 0

Solving
4 + -1w = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1w = 0 + -4
-1w = 0 + -4

Combine like terms: 0 + -4 = -4
-1w = -4

Divide each side by '-1'.
w = 4

Simplifying
w = 4
Solution
w = {4, 4}