192=2w^2+20w

Solution for 192=2w^2+20w equation:

Simplifying
192 = 2w2 + 20w

Reorder the terms:
192 = 20w + 2w2

Solving
192 = 20w + 2w2

Solving for variable 'w'.

Reorder the terms:
192 + -20w + -2w2 = 20w + -20w + 2w2 + -2w2

Combine like terms: 20w + -20w = 0
192 + -20w + -2w2 = 0 + 2w2 + -2w2
192 + -20w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
192 + -20w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(96 + -10w + -1w2) = 0

Factor a trinomial.
2((6 + -1w)(16 + w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
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 = {6, -16}