r^2+2r=2+3r

Solution for r^2+2r=2+3r equation:

Simplifying
r2 + 2r = 2 + 3r

Reorder the terms:
2r + r2 = 2 + 3r

Solving
2r + r2 = 2 + 3r

Solving for variable 'r'.

Reorder the terms:
-2 + 2r + -3r + r2 = 2 + 3r + -2 + -3r

Combine like terms: 2r + -3r = -1r
-2 + -1r + r2 = 2 + 3r + -2 + -3r

Reorder the terms:
-2 + -1r + r2 = 2 + -2 + 3r + -3r

Combine like terms: 2 + -2 = 0
-2 + -1r + r2 = 0 + 3r + -3r
-2 + -1r + r2 = 3r + -3r

Combine like terms: 3r + -3r = 0
-2 + -1r + r2 = 0

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

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

Simplifying
-1 + -1r = 0

Solving
-1 + -1r = 0

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

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

Combine like terms: -1 + 1 = 0
0 + -1r = 0 + 1
-1r = 0 + 1

Combine like terms: 0 + 1 = 1
-1r = 1

Divide each side by '-1'.
r = -1

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

Simplifying
2 + -1r = 0

Solving
2 + -1r = 0

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

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

Combine like terms: 2 + -2 = 0
0 + -1r = 0 + -2
-1r = 0 + -2

Combine like terms: 0 + -2 = -2
-1r = -2

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-1, 2}