r^2+15ry+50y^2=0

Solution for r^2+15ry+50y^2=0 equation:

Simplifying
r2 + 15ry + 50y2 = 0

Reorder the terms:
15ry + r2 + 50y2 = 0

Solving
15ry + r2 + 50y2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + 5y)(r + 10y) = 0

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

Simplifying
r + 5y = 0

Solving
r + 5y = 0

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

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

Combine like terms: 5y + -5y = 0
r + 0 = 0 + -5y
r = 0 + -5y
Remove the zero:
r = -5y

Simplifying
r = -5y
Subproblem 2
Set the factor '(r + 10y)' equal to zero and attempt to solve:

Simplifying
r + 10y = 0

Solving
r + 10y = 0

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

Add '-10y' to each side of the equation.
r + 10y + -10y = 0 + -10y

Combine like terms: 10y + -10y = 0
r + 0 = 0 + -10y
r = 0 + -10y
Remove the zero:
r = -10y

Simplifying
r = -10y
Solution
r = {-5y, -10y}