24w+36=-3w^2

Solution for 24w+36=-3w^2 equation:

Simplifying
24w + 36 = -3w2

Reorder the terms:
36 + 24w = -3w2

Solving
36 + 24w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
36 + 24w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(12 + 8w + w2) = 0

Factor a trinomial.
3((6 + w)(2 + w)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
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
Solution
w = {-6, -2}