9w^2+21w+12=0

Solution for 9w^2+21w+12=0 equation:

Simplifying
9w2 + 21w + 12 = 0

Reorder the terms:
12 + 21w + 9w2 = 0

Solving
12 + 21w + 9w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 7w + 3w2) = 0

Factor a trinomial.
3((4 + 3w)(1 + w)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + 3w)' equal to zero and attempt to solve:

Simplifying
4 + 3w = 0

Solving
4 + 3w = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3w = 0 + -4
3w = 0 + -4

Combine like terms: 0 + -4 = -4
3w = -4

Divide each side by '3'.
w = -1.333333333

Simplifying
w = -1.333333333
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 = {-1.333333333, -1}