3r^2+4rs-20s^2=0

Solution for 3r^2+4rs-20s^2=0 equation:

Simplifying
3r2 + 4rs + -20s2 = 0

Reorder the terms:
4rs + 3r2 + -20s2 = 0

Solving
4rs + 3r2 + -20s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(r + -2s)(3r + 10s) = 0

Subproblem 1
Set the factor '(r + -2s)' equal to zero and attempt to solve:

Simplifying
r + -2s = 0

Solving
r + -2s = 0

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

Add '2s' to each side of the equation.
r + -2s + 2s = 0 + 2s

Combine like terms: -2s + 2s = 0
r + 0 = 0 + 2s
r = 0 + 2s
Remove the zero:
r = 2s

Simplifying
r = 2s
Subproblem 2
Set the factor '(3r + 10s)' equal to zero and attempt to solve:

Simplifying
3r + 10s = 0

Solving
3r + 10s = 0

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

Add '-10s' to each side of the equation.
3r + 10s + -10s = 0 + -10s

Combine like terms: 10s + -10s = 0
3r + 0 = 0 + -10s
3r = 0 + -10s
Remove the zero:
3r = -10s

Divide each side by '3'.
r = -3.333333333s

Simplifying
r = -3.333333333s
Solution
r = {2s, -3.333333333s}