75w^2-10w-5=0

Solution for 75w^2-10w-5=0 equation:

Simplifying
75w2 + -10w + -5 = 0

Reorder the terms:
-5 + -10w + 75w2 = 0

Solving
-5 + -10w + 75w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + -2w + 15w2) = 0

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

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

Simplifying
-1 + -5w = 0

Solving
-1 + -5w = 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 + -5w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -5w = 0 + 1
-5w = 0 + 1

Combine like terms: 0 + 1 = 1
-5w = 1

Divide each side by '-5'.
w = -0.2

Simplifying
w = -0.2
Subproblem 2
Set the factor '(1 + -3w)' equal to zero and attempt to solve:

Simplifying
1 + -3w = 0

Solving
1 + -3w = 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 + -3w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3w = 0 + -1
-3w = 0 + -1

Combine like terms: 0 + -1 = -1
-3w = -1

Divide each side by '-3'.
w = 0.3333333333

Simplifying
w = 0.3333333333
Solution
w = {-0.2, 0.3333333333}