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

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


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

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

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

Reorder the terms:
(-9rs + rs + 3r2 + -3s2) = 0

Combine like terms: -9rs + rs = -8rs
(-8rs + 3r2 + -3s2) = 0

Solving
-8rs + 3r2 + -3s2 = 0

Solving for variable 'r'.

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


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

Simplifying
r + -3s = 0

Solving
r + -3s = 0

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

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

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

Simplifying
r = 3s

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

Simplifying
3r + s = 0

Solving
3r + s = 0

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

Add '-1s' to each side of the equation.
3r + s + -1s = 0 + -1s

Combine like terms: s + -1s = 0
3r + 0 = 0 + -1s
3r = 0 + -1s
Remove the zero:
3r = -1s

Divide each side by '3'.
r = -0.3333333333s

Simplifying
r = -0.3333333333s
Solution
r = {3s, -0.3333333333s}

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