48=w(w-2)

Solution for 48=w(w-2) equation:

Simplifying
48 = w(w + -2)

Reorder the terms:
48 = w(-2 + w)
48 = (-2 * w + w * w)
48 = (-2w + w2)

Solving
48 = -2w + w2

Solving for variable 'w'.

Reorder the terms:
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.
(8 + -1w)(6 + w) = 0

Subproblem 1
Set the factor '(8 + -1w)' equal to zero and attempt to solve:

Simplifying
8 + -1w = 0

Solving
8 + -1w = 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 + -1w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1w = 0 + -8
-1w = 0 + -8

Combine like terms: 0 + -8 = -8
-1w = -8

Divide each side by '-1'.
w = 8

Simplifying
w = 8
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 = {8, -6}