5r^2+50r+125=0

Solution for 5r^2+50r+125=0 equation:

Simplifying
5r2 + 50r + 125 = 0

Reorder the terms:
125 + 50r + 5r2 = 0

Solving
125 + 50r + 5r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '5'.
5(25 + 10r + r2) = 0

Factor a trinomial.
5((5 + r)(5 + r)) = 0

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

Simplifying
5 + r = 0

Solving
5 + r = 0

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

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

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

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

Simplifying
5 + r = 0

Solving
5 + r = 0

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

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

Combine like terms: 5 + -5 = 0
0 + r = 0 + -5
r = 0 + -5

Combine like terms: 0 + -5 = -5
r = -5

Simplifying
r = -5
Solution
r = {-5, -5}