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

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

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

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

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

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

Multiply (3 + 2r) * (1 + r)
3r + 3r2 = (3(1 + r) + 2r * (1 + r))
3r + 3r2 = ((1 * 3 + r * 3) + 2r * (1 + r))
3r + 3r2 = ((3 + 3r) + 2r * (1 + r))
3r + 3r2 = (3 + 3r + (1 * 2r + r * 2r))
3r + 3r2 = (3 + 3r + (2r + 2r2))

Combine like terms: 3r + 2r = 5r
3r + 3r2 = (3 + 5r + 2r2)

Solving
3r + 3r2 = 3 + 5r + 2r2

Solving for variable 'r'.

Reorder the terms:
-3 + 3r + -5r + 3r2 + -2r2 = 3 + 5r + 2r2 + -3 + -5r + -2r2

Combine like terms: 3r + -5r = -2r
-3 + -2r + 3r2 + -2r2 = 3 + 5r + 2r2 + -3 + -5r + -2r2

Combine like terms: 3r2 + -2r2 = 1r2
-3 + -2r + 1r2 = 3 + 5r + 2r2 + -3 + -5r + -2r2

Reorder the terms:
-3 + -2r + 1r2 = 3 + -3 + 5r + -5r + 2r2 + -2r2

Combine like terms: 3 + -3 = 0
-3 + -2r + 1r2 = 0 + 5r + -5r + 2r2 + -2r2
-3 + -2r + 1r2 = 5r + -5r + 2r2 + -2r2

Combine like terms: 5r + -5r = 0
-3 + -2r + 1r2 = 0 + 2r2 + -2r2
-3 + -2r + 1r2 = 2r2 + -2r2

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

Factor a trinomial.
(-1 + -1r)(3 + -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 '(3 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

Solving
3 + -1r = 0

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

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {-1, 3}