2w^2+(-2)w=24

Solution for 2w^2+(-2)w=24 equation:

Simplifying
2w2 + (-2) * w = 24

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

Solving
-2w + 2w2 = 24

Solving for variable 'w'.

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

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

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

Factor a trinomial.
2((-3 + -1w)(4 + -1w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1w)' equal to zero and attempt to solve:

Simplifying
-3 + -1w = 0

Solving
-3 + -1w = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1w = 0 + 3
-1w = 0 + 3

Combine like terms: 0 + 3 = 3
-1w = 3

Divide each side by '-1'.
w = -3

Simplifying
w = -3
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 = {-3, 4}