(2r-s)(3r+2s)=

Solution for (2r-s)(3r+2s)= equation:

Simplifying
(2r + -1s)(3r + 2s) = 0

Multiply (2r + -1s) * (3r + 2s)
(2r * (3r + 2s) + -1s * (3r + 2s)) = 0
((3r * 2r + 2s * 2r) + -1s * (3r + 2s)) = 0

Reorder the terms:
((4rs + 6r2) + -1s * (3r + 2s)) = 0
((4rs + 6r2) + -1s * (3r + 2s)) = 0
(4rs + 6r2 + (3r * -1s + 2s * -1s)) = 0
(4rs + 6r2 + (-3rs + -2s2)) = 0

Reorder the terms:
(4rs + -3rs + 6r2 + -2s2) = 0

Combine like terms: 4rs + -3rs = 1rs
(1rs + 6r2 + -2s2) = 0

Solving
1rs + 6r2 + -2s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(2r + -1s)(3r + 2s) = 0

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

Simplifying
2r + -1s = 0

Solving
2r + -1s = 0

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

Add 's' to each side of the equation.
2r + -1s + s = 0 + s

Combine like terms: -1s + s = 0
2r + 0 = 0 + s
2r = 0 + s
Remove the zero:
2r = s

Divide each side by '2'.
r = 0.5s

Simplifying
r = 0.5s
Subproblem 2
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
Solution
r = {0.5s, -0.6666666667s}