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

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

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

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

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

Reorder the terms:
(-1rs + 2rs + r2 + -2s2) = 0

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

Solving
1rs + r2 + -2s2 = 0

Solving for variable 'r'.

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

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

Simplifying
r + -1s = 0

Solving
r + -1s = 0

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

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

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

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

Simplifying
r + 2s = 0

Solving
r + 2s = 0

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

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

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

Simplifying
r = -2s
Solution
r = {s, -2s}