w(w+2)2=48

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

Simplifying
w(w + 2) * 2 = 48

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

Reorder the terms for easier multiplication:
2w(2 + w) = 48
(2 * 2w + w * 2w) = 48
(4w + 2w2) = 48

Solving
4w + 2w2 = 48

Solving for variable 'w'.

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

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

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

Factor a trinomial.
2((-6 + -1w)(4 + -1w)) = 0

Ignore the factor 2.
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 '(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 = {-6, 4}