r(r+3)-2(r+1)=

Solution for r(r+3)-2(r+1)= equation:

Simplifying
r(r + 3) + -2(r + 1) = 0

Reorder the terms:
r(3 + r) + -2(r + 1) = 0
(3 * r + r * r) + -2(r + 1) = 0
(3r + r2) + -2(r + 1) = 0

Reorder the terms:
3r + r2 + -2(1 + r) = 0
3r + r2 + (1 * -2 + r * -2) = 0
3r + r2 + (-2 + -2r) = 0

Reorder the terms:
-2 + 3r + -2r + r2 = 0

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

Solving
-2 + 1r + r2 = 0

Solving for variable 'r'.

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

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