30w^2-w-20=0

Solution for 30w^2-w-20=0 equation:

Simplifying
30w2 + -1w + -20 = 0

Reorder the terms:
-20 + -1w + 30w2 = 0

Solving
-20 + -1w + 30w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-4 + -5w)(5 + -6w) = 0

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

Simplifying
-4 + -5w = 0

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

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

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

Divide each side by '-5'.
w = -0.8

Simplifying
w = -0.8
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 = {-0.8, 0.8333333333}