12w^2-28w-5=0

Solution for 12w^2-28w-5=0 equation:

Simplifying
12w2 + -28w + -5 = 0

Reorder the terms:
-5 + -28w + 12w2 = 0

Solving
-5 + -28w + 12w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -6w)(5 + -2w) = 0

Subproblem 1
Set the factor '(-1 + -6w)' equal to zero and attempt to solve:

Simplifying
-1 + -6w = 0

Solving
-1 + -6w = 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 + -6w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6w = 0 + 1
-6w = 0 + 1

Combine like terms: 0 + 1 = 1
-6w = 1

Divide each side by '-6'.
w = -0.1666666667

Simplifying
w = -0.1666666667
Subproblem 2
Set the factor '(5 + -2w)' equal to zero and attempt to solve:

Simplifying
5 + -2w = 0

Solving
5 + -2w = 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 + -2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2w = 0 + -5
-2w = 0 + -5

Combine like terms: 0 + -5 = -5
-2w = -5

Divide each side by '-2'.
w = 2.5

Simplifying
w = 2.5
Solution
w = {-0.1666666667, 2.5}