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

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

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

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

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

Multiply (3 + 2r) * (-1 + 2r)
(3(-1 + 2r) + 2r * (-1 + 2r)) = -3(r + 1)
((-1 * 3 + 2r * 3) + 2r * (-1 + 2r)) = -3(r + 1)
((-3 + 6r) + 2r * (-1 + 2r)) = -3(r + 1)
(-3 + 6r + (-1 * 2r + 2r * 2r)) = -3(r + 1)
(-3 + 6r + (-2r + 4r2)) = -3(r + 1)

Combine like terms: 6r + -2r = 4r
(-3 + 4r + 4r2) = -3(r + 1)

Reorder the terms:
-3 + 4r + 4r2 = -3(1 + r)
-3 + 4r + 4r2 = (1 * -3 + r * -3)
-3 + 4r + 4r2 = (-3 + -3r)

Add '3' to each side of the equation.
-3 + 4r + 3 + 4r2 = -3 + 3 + -3r

Reorder the terms:
-3 + 3 + 4r + 4r2 = -3 + 3 + -3r

Combine like terms: -3 + 3 = 0
0 + 4r + 4r2 = -3 + 3 + -3r
4r + 4r2 = -3 + 3 + -3r

Combine like terms: -3 + 3 = 0
4r + 4r2 = 0 + -3r
4r + 4r2 = -3r

Solving
4r + 4r2 = -3r

Solving for variable 'r'.

Reorder the terms:
4r + 3r + 4r2 = -3r + 3r

Combine like terms: 4r + 3r = 7r
7r + 4r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
7r + 4r2 = 0

Factor out the Greatest Common Factor (GCF), 'r'.
r(7 + 4r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
Subproblem 2
Set the factor '(7 + 4r)' equal to zero and attempt to solve:

Simplifying
7 + 4r = 0

Solving
7 + 4r = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4r = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4r = 0 + -7
4r = 0 + -7

Combine like terms: 0 + -7 = -7
4r = -7

Divide each side by '4'.
r = -1.75

Simplifying
r = -1.75
Solution
r = {0, -1.75}