5w^2-4w-12=0

Solution for 5w^2-4w-12=0 equation:

Simplifying
5w2 + -4w + -12 = 0

Reorder the terms:
-12 + -4w + 5w2 = 0

Solving
-12 + -4w + 5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(-6 + -5w)' equal to zero and attempt to solve:

Simplifying
-6 + -5w = 0

Solving
-6 + -5w = 0

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

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

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

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

Divide each side by '-5'.
w = -1.2

Simplifying
w = -1.2
Subproblem 2
Set the factor '(2 + -1w)' equal to zero and attempt to solve:

Simplifying
2 + -1w = 0

Solving
2 + -1w = 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 + -1w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1w = 0 + -2
-1w = 0 + -2

Combine like terms: 0 + -2 = -2
-1w = -2

Divide each side by '-1'.
w = 2

Simplifying
w = 2
Solution
w = {-1.2, 2}