0=2w+w^2-48

Solution for 0=2w+w^2-48 equation:

Simplifying
0 = 2w + w2 + -48

Reorder the terms:
0 = -48 + 2w + w2

Solving
0 = -48 + 2w + w2

Solving for variable 'w'.

Combine like terms: 0 + 48 = 48
48 + -2w + -1w2 = -48 + 2w + w2 + 48 + -2w + -1w2

Reorder the terms:
48 + -2w + -1w2 = -48 + 48 + 2w + -2w + w2 + -1w2

Combine like terms: -48 + 48 = 0
48 + -2w + -1w2 = 0 + 2w + -2w + w2 + -1w2
48 + -2w + -1w2 = 2w + -2w + w2 + -1w2

Combine like terms: 2w + -2w = 0
48 + -2w + -1w2 = 0 + w2 + -1w2
48 + -2w + -1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
48 + -2w + -1w2 = 0

Factor a trinomial.
(6 + -1w)(8 + w) = 0

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 '(8 + w)' equal to zero and attempt to solve:

Simplifying
8 + w = 0

Solving
8 + w = 0

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

Add '-8' to each side of the equation.
8 + -8 + w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + w = 0 + -8
w = 0 + -8

Combine like terms: 0 + -8 = -8
w = -8

Simplifying
w = -8
Solution
w = {6, -8}