(3r+2s)(4r-3s)=

Solution for (3r+2s)(4r-3s)= equation:

Simplifying
(3r + 2s)(4r + -3s) = 0

Multiply (3r + 2s) * (4r + -3s)
(3r * (4r + -3s) + 2s * (4r + -3s)) = 0
((4r * 3r + -3s * 3r) + 2s * (4r + -3s)) = 0

Reorder the terms:
((-9rs + 12r2) + 2s * (4r + -3s)) = 0
((-9rs + 12r2) + 2s * (4r + -3s)) = 0
(-9rs + 12r2 + (4r * 2s + -3s * 2s)) = 0
(-9rs + 12r2 + (8rs + -6s2)) = 0

Reorder the terms:
(-9rs + 8rs + 12r2 + -6s2) = 0

Combine like terms: -9rs + 8rs = -1rs
(-1rs + 12r2 + -6s2) = 0

Solving
-1rs + 12r2 + -6s2 = 0

Solving for variable 'r'.

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

Subproblem 1
Set the factor '(4r + -3s)' equal to zero and attempt to solve:

Simplifying
4r + -3s = 0

Solving
4r + -3s = 0

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

Add '3s' to each side of the equation.
4r + -3s + 3s = 0 + 3s

Combine like terms: -3s + 3s = 0
4r + 0 = 0 + 3s
4r = 0 + 3s
Remove the zero:
4r = 3s

Divide each side by '4'.
r = 0.75s

Simplifying
r = 0.75s
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 = {0.75s, -0.6666666667s}