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

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

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

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

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

Reorder the terms:
(-6rs + -6rs + 9r2 + 4s2) = 0

Combine like terms: -6rs + -6rs = -12rs
(-12rs + 9r2 + 4s2) = 0

Solving
-12rs + 9r2 + 4s2 = 0

Solving for variable 'r'.

Factor a trinomial.
(3r + -2s)(3r + -2s) = 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 '(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 = {0.6666666667s, 0.6666666667s}