-2w^2-24w+200=72

Solution for -2w^2-24w+200=72 equation:

Simplifying
-2w2 + -24w + 200 = 72

Reorder the terms:
200 + -24w + -2w2 = 72

Solving
200 + -24w + -2w2 = 72

Solving for variable 'w'.

Reorder the terms:
200 + -72 + -24w + -2w2 = 72 + -72

Combine like terms: 200 + -72 = 128
128 + -24w + -2w2 = 72 + -72

Combine like terms: 72 + -72 = 0
128 + -24w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(64 + -12w + -1w2) = 0

Factor a trinomial.
2((4 + -1w)(16 + w)) = 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 '(16 + w)' equal to zero and attempt to solve:

Simplifying
16 + w = 0

Solving
16 + w = 0

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

Add '-16' to each side of the equation.
16 + -16 + w = 0 + -16

Combine like terms: 16 + -16 = 0
0 + w = 0 + -16
w = 0 + -16

Combine like terms: 0 + -16 = -16
w = -16

Simplifying
w = -16
Solution
w = {4, -16}