5b^2+75b+180=0

Solution for 5b^2+75b+180=0 equation:

Simplifying
5b2 + 75b + 180 = 0

Reorder the terms:
180 + 75b + 5b2 = 0

Solving
180 + 75b + 5b2 = 0

Solving for variable 'b'.

Factor out the Greatest Common Factor (GCF), '5'.
5(36 + 15b + b2) = 0

Factor a trinomial.
5((12 + b)(3 + b)) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(12 + b)' equal to zero and attempt to solve:

Simplifying
12 + b = 0

Solving
12 + b = 0

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

Add '-12' to each side of the equation.
12 + -12 + b = 0 + -12

Combine like terms: 12 + -12 = 0
0 + b = 0 + -12
b = 0 + -12

Combine like terms: 0 + -12 = -12
b = -12

Simplifying
b = -12
Subproblem 2
Set the factor '(3 + b)' equal to zero and attempt to solve:

Simplifying
3 + b = 0

Solving
3 + b = 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 + b = 0 + -3

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

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

Simplifying
b = -3
Solution
b = {-12, -3}