w(w-2)=48

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

Simplifying
w(w + -2) = 48

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

Solving
-2w + w2 = 48

Solving for variable 'w'.

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

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

Factor a trinomial.
(-6 + -1w)(8 + -1w) = 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 + -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
Solution
w = {-6, 8}