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

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

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

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

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

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

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

Reorder the terms:
-3 + 4r + 4r2 = -1(-2 + 3r)
-3 + 4r + 4r2 = (-2 * -1 + 3r * -1)
-3 + 4r + 4r2 = (2 + -3r)

Solving
-3 + 4r + 4r2 = 2 + -3r

Solving for variable 'r'.

Reorder the terms:
-3 + -2 + 4r + 3r + 4r2 = 2 + -3r + -2 + 3r

Combine like terms: -3 + -2 = -5
-5 + 4r + 3r + 4r2 = 2 + -3r + -2 + 3r

Combine like terms: 4r + 3r = 7r
-5 + 7r + 4r2 = 2 + -3r + -2 + 3r

Reorder the terms:
-5 + 7r + 4r2 = 2 + -2 + -3r + 3r

Combine like terms: 2 + -2 = 0
-5 + 7r + 4r2 = 0 + -3r + 3r
-5 + 7r + 4r2 = -3r + 3r

Combine like terms: -3r + 3r = 0
-5 + 7r + 4r2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
-1.25 + 1.75r + r2 = 0

Move the constant term to the right:

Add '1.25' to each side of the equation.
-1.25 + 1.75r + 1.25 + r2 = 0 + 1.25

Reorder the terms:
-1.25 + 1.25 + 1.75r + r2 = 0 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + 1.75r + r2 = 0 + 1.25
1.75r + r2 = 0 + 1.25

Combine like terms: 0 + 1.25 = 1.25
1.75r + r2 = 1.25

The r term is 1.75r.  Take half its coefficient (0.875).
Square it (0.765625) and add it to both sides.

Add '0.765625' to each side of the equation.
1.75r + 0.765625 + r2 = 1.25 + 0.765625

Reorder the terms:
0.765625 + 1.75r + r2 = 1.25 + 0.765625

Combine like terms: 1.25 + 0.765625 = 2.015625
0.765625 + 1.75r + r2 = 2.015625

Factor a perfect square on the left side:
(r + 0.875)(r + 0.875) = 2.015625

Calculate the square root of the right side: 1.419727086

Break this problem into two subproblems by setting 
(r + 0.875) equal to 1.419727086 and -1.419727086.

Subproblem 1
r + 0.875 = 1.419727086

Simplifying
r + 0.875 = 1.419727086

Reorder the terms:
0.875 + r = 1.419727086

Solving
0.875 + r = 1.419727086

Solving for variable 'r'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + r = 1.419727086 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + r = 1.419727086 + -0.875
r = 1.419727086 + -0.875

Combine like terms: 1.419727086 + -0.875 = 0.544727086
r = 0.544727086

Simplifying
r = 0.544727086

Subproblem 2
r + 0.875 = -1.419727086

Simplifying
r + 0.875 = -1.419727086

Reorder the terms:
0.875 + r = -1.419727086

Solving
0.875 + r = -1.419727086

Solving for variable 'r'.

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

Add '-0.875' to each side of the equation.
0.875 + -0.875 + r = -1.419727086 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + r = -1.419727086 + -0.875
r = -1.419727086 + -0.875

Combine like terms: -1.419727086 + -0.875 = -2.294727086
r = -2.294727086

Simplifying
r = -2.294727086

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.544727086, -2.294727086}