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

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

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

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

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

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

Combine like terms: rs + 2rs = 3rs
(3rs + 2r2 + s2) = 0

Solving
3rs + 2r2 + s2 = 0

Solving for variable 'r'.

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

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

Simplifying
2r + s = 0

Solving
2r + s = 0

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

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

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

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

Simplifying
r = -0.5s
Subproblem 2
Set the factor '(r + s)' equal to zero and attempt to solve:

Simplifying
r + s = 0

Solving
r + s = 0

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

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

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

Simplifying
r = -1s
Solution
r = {-0.5s, -1s}