10r^2+4rs+15rs+6s^2=

Solution for 10r^2+4rs+15rs+6s^2= equation:

Simplifying
10r2 + 4rs + 15rs + 6s2 = 0

Reorder the terms:
4rs + 15rs + 10r2 + 6s2 = 0

Combine like terms: 4rs + 15rs = 19rs
19rs + 10r2 + 6s2 = 0

Solving
19rs + 10r2 + 6s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(5r + 2s)(2r + 3s) = 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 '(2r + 3s)' equal to zero and attempt to solve:

Simplifying
2r + 3s = 0

Solving
2r + 3s = 0

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

Add '-3s' to each side of the equation.
2r + 3s + -3s = 0 + -3s

Combine like terms: 3s + -3s = 0
2r + 0 = 0 + -3s
2r = 0 + -3s
Remove the zero:
2r = -3s

Divide each side by '2'.
r = -1.5s

Simplifying
r = -1.5s
Solution
r = {-0.4s, -1.5s}