12r^2+7rs-10s^2=

Solution for 12r^2+7rs-10s^2= equation:

Simplifying
12r2 + 7rs + -10s2 = 0

Reorder the terms:
7rs + 12r2 + -10s2 = 0

Solving
7rs + 12r2 + -10s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + -2s)(4r + 5s) = 0

Subproblem 1
Set the factor '(3r + -2s)' equal to zero and attempt to solve:

Simplifying
3r + -2s = 0

Solving
3r + -2s = 0

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

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

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

Divide each side by '3'.
r = 0.6666666667s

Simplifying
r = 0.6666666667s
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 = {0.6666666667s, -1.25s}