12w^2+28w+15=0

Solution for 12w^2+28w+15=0 equation:

Simplifying
12w2 + 28w + 15 = 0

Reorder the terms:
15 + 28w + 12w2 = 0

Solving
15 + 28w + 12w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + 2w)(5 + 6w) = 0

Subproblem 1
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Subproblem 2
Set the factor '(5 + 6w)' equal to zero and attempt to solve:

Simplifying
5 + 6w = 0

Solving
5 + 6w = 0

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

Add '-5' to each side of the equation.
5 + -5 + 6w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 6w = 0 + -5
6w = 0 + -5

Combine like terms: 0 + -5 = -5
6w = -5

Divide each side by '6'.
w = -0.8333333333

Simplifying
w = -0.8333333333
Solution
w = {-1.5, -0.8333333333}