5w^2+10w-75=0

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

Simplifying
5w2 + 10w + -75 = 0

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

Solving
-75 + 10w + 5w2 = 0

Solving for variable 'w'.

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

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

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

Simplifying
-5 + -1w = 0

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

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

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

Divide each side by '-1'.
w = -5

Simplifying
w = -5
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1w = 0 + -3

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

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

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-5, 3}