w(2w+8)=24

Solution for w(2w+8)=24 equation:

Simplifying
w(2w + 8) = 24

Reorder the terms:
w(8 + 2w) = 24
(8 * w + 2w * w) = 24
(8w + 2w2) = 24

Solving
8w + 2w2 = 24

Solving for variable 'w'.

Reorder the terms:
-24 + 8w + 2w2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 8w + 2w2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4w + w2) = 0

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

Simplifying
2 + -1w = 0

Solving
2 + -1w = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1w = 0 + -2

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

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

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-6, 2}