20r^2+33rs+10s^2=

Solution for 20r^2+33rs+10s^2= equation:

Simplifying
20r2 + 33rs + 10s2 = 0

Reorder the terms:
33rs + 20r2 + 10s2 = 0

Solving
33rs + 20r2 + 10s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5r + 2s)(4r + 5s) = 0

Subproblem 1
Set the factor '(5r + 2s)' equal to zero and attempt to solve:

Simplifying
5r + 2s = 0

Solving
5r + 2s = 0

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

Add '-2s' to each side of the equation.
5r + 2s + -2s = 0 + -2s

Combine like terms: 2s + -2s = 0
5r + 0 = 0 + -2s
5r = 0 + -2s
Remove the zero:
5r = -2s

Divide each side by '5'.
r = -0.4s

Simplifying
r = -0.4s
Subproblem 2
Set the factor '(4r + 5s)' equal to zero and attempt to solve:

Simplifying
4r + 5s = 0

Solving
4r + 5s = 0

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

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

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

Divide each side by '4'.
r = -1.25s

Simplifying
r = -1.25s
Solution
r = {-0.4s, -1.25s}