48=4w+2w^2

Solution for 48=4w+2w^2 equation:

Simplifying
48 = 4w + 2w2

Solving
48 = 4w + 2w2

Solving for variable 'w'.

Reorder the terms:
48 + -4w + -2w2 = 4w + -4w + 2w2 + -2w2

Combine like terms: 4w + -4w = 0
48 + -4w + -2w2 = 0 + 2w2 + -2w2
48 + -4w + -2w2 = 2w2 + -2w2

Combine like terms: 2w2 + -2w2 = 0
48 + -4w + -2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(24 + -2w + -1w2) = 0

Factor a trinomial.
2((4 + -1w)(6 + 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 '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 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 + w = 0 + -6

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

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

Simplifying
w = -6
Solution
w = {4, -6}