3w(4w+12)=-24

Solution for 3w(4w+12)=-24 equation:

Simplifying
3w(4w + 12) = -24

Reorder the terms:
3w(12 + 4w) = -24
(12 * 3w + 4w * 3w) = -24
(36w + 12w2) = -24

Solving
36w + 12w2 = -24

Solving for variable 'w'.

Reorder the terms:
24 + 36w + 12w2 = -24 + 24

Combine like terms: -24 + 24 = 0
24 + 36w + 12w2 = 0

Factor out the Greatest Common Factor (GCF), '12'.
12(2 + 3w + w2) = 0

Factor a trinomial.
12((2 + w)(1 + w)) = 0

Ignore the factor 12.
Subproblem 1
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 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 + w = 0 + -2

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

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

Simplifying
w = -2
Subproblem 2
Set the factor '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

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

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

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

Simplifying
w = -1
Solution
w = {-2, -1}