12w^2-3w-15=0

Solution for 12w^2-3w-15=0 equation:

Simplifying
12w2 + -3w + -15 = 0

Reorder the terms:
-15 + -3w + 12w2 = 0

Solving
-15 + -3w + 12w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + -1w + 4w2) = 0

Factor a trinomial.
3((-1 + -1w)(5 + -4w)) = 0

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

Simplifying
-1 + -1w = 0

Solving
-1 + -1w = 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 + -1w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1w = 0 + 1
-1w = 0 + 1

Combine like terms: 0 + 1 = 1
-1w = 1

Divide each side by '-1'.
w = -1

Simplifying
w = -1
Subproblem 2
Set the factor '(5 + -4w)' equal to zero and attempt to solve:

Simplifying
5 + -4w = 0

Solving
5 + -4w = 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 + -4w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -4w = 0 + -5
-4w = 0 + -5

Combine like terms: 0 + -5 = -5
-4w = -5

Divide each side by '-4'.
w = 1.25

Simplifying
w = 1.25
Solution
w = {-1, 1.25}