9w+6=-3w^2

Solution for 9w+6=-3w^2 equation:

Simplifying
9w + 6 = -3w2

Reorder the terms:
6 + 9w = -3w2

Solving
6 + 9w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
6 + 9w + 3w2 = 0

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

Factor a trinomial.
3((2 + w)(1 + w)) = 0

Ignore the factor 3.
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}