12w+9=-3w^2

Solution for 12w+9=-3w^2 equation:

Simplifying
12w + 9 = -3w2

Reorder the terms:
9 + 12w = -3w2

Solving
9 + 12w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
9 + 12w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 4w + w2) = 0

Factor a trinomial.
3((3 + w)(1 + w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

Solving
3 + w = 0

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

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + w = 0 + -3
w = 0 + -3

Combine like terms: 0 + -3 = -3
w = -3

Simplifying
w = -3
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 = {-3, -1}