25b^2+110b-75=0

Solution for 25b^2+110b-75=0 equation:

Simplifying
25b2 + 110b + -75 = 0

Reorder the terms:
-75 + 110b + 25b2 = 0

Solving
-75 + 110b + 25b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-15 + 22b + 5b2) = 0

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

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

Simplifying
-5 + -1b = 0

Solving
-5 + -1b = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1b = 0 + 5

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

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

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

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

Simplifying
3 + -5b = 0

Solving
3 + -5b = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5b = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5b = 0 + -3
-5b = 0 + -3

Combine like terms: 0 + -3 = -3
-5b = -3

Divide each side by '-5'.
b = 0.6

Simplifying
b = 0.6
Solution
b = {-5, 0.6}