12r^2+5ry-25y^2=0

Solution for 12r^2+5ry-25y^2=0 equation:

Simplifying
12r2 + 5ry + -25y2 = 0

Reorder the terms:
5ry + 12r2 + -25y2 = 0

Solving
5ry + 12r2 + -25y2 = 0

Solving for variable 'r'.

Factor a trinomial.
(4r + -5y)(3r + 5y) = 0

Subproblem 1
Set the factor '(4r + -5y)' equal to zero and attempt to solve:

Simplifying
4r + -5y = 0

Solving
4r + -5y = 0

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

Add '5y' to each side of the equation.
4r + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
4r + 0 = 0 + 5y
4r = 0 + 5y
Remove the zero:
4r = 5y

Divide each side by '4'.
r = 1.25y

Simplifying
r = 1.25y
Subproblem 2
Set the factor '(3r + 5y)' equal to zero and attempt to solve:

Simplifying
3r + 5y = 0

Solving
3r + 5y = 0

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

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

Combine like terms: 5y + -5y = 0
3r + 0 = 0 + -5y
3r = 0 + -5y
Remove the zero:
3r = -5y

Divide each side by '3'.
r = -1.666666667y

Simplifying
r = -1.666666667y
Solution
r = {1.25y, -1.666666667y}