(3r-7)(r+2)=(2r-1)(r-3)

Solution for (3r-7)(r+2)=(2r-1)(r-3) equation:

Simplifying
(3r + -7)(r + 2) = (2r + -1)(r + -3)

Reorder the terms:
(-7 + 3r)(r + 2) = (2r + -1)(r + -3)

Reorder the terms:
(-7 + 3r)(2 + r) = (2r + -1)(r + -3)

Multiply (-7 + 3r) * (2 + r)
(-7(2 + r) + 3r * (2 + r)) = (2r + -1)(r + -3)
((2 * -7 + r * -7) + 3r * (2 + r)) = (2r + -1)(r + -3)
((-14 + -7r) + 3r * (2 + r)) = (2r + -1)(r + -3)
(-14 + -7r + (2 * 3r + r * 3r)) = (2r + -1)(r + -3)
(-14 + -7r + (6r + 3r2)) = (2r + -1)(r + -3)

Combine like terms: -7r + 6r = -1r
(-14 + -1r + 3r2) = (2r + -1)(r + -3)

Reorder the terms:
-14 + -1r + 3r2 = (-1 + 2r)(r + -3)

Reorder the terms:
-14 + -1r + 3r2 = (-1 + 2r)(-3 + r)

Multiply (-1 + 2r) * (-3 + r)
-14 + -1r + 3r2 = (-1(-3 + r) + 2r * (-3 + r))
-14 + -1r + 3r2 = ((-3 * -1 + r * -1) + 2r * (-3 + r))
-14 + -1r + 3r2 = ((3 + -1r) + 2r * (-3 + r))
-14 + -1r + 3r2 = (3 + -1r + (-3 * 2r + r * 2r))
-14 + -1r + 3r2 = (3 + -1r + (-6r + 2r2))

Combine like terms: -1r + -6r = -7r
-14 + -1r + 3r2 = (3 + -7r + 2r2)

Solving
-14 + -1r + 3r2 = 3 + -7r + 2r2

Solving for variable 'r'.

Reorder the terms:
-14 + -3 + -1r + 7r + 3r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: -14 + -3 = -17
-17 + -1r + 7r + 3r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: -1r + 7r = 6r
-17 + 6r + 3r2 + -2r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Combine like terms: 3r2 + -2r2 = 1r2
-17 + 6r + 1r2 = 3 + -7r + 2r2 + -3 + 7r + -2r2

Reorder the terms:
-17 + 6r + 1r2 = 3 + -3 + -7r + 7r + 2r2 + -2r2

Combine like terms: 3 + -3 = 0
-17 + 6r + 1r2 = 0 + -7r + 7r + 2r2 + -2r2
-17 + 6r + 1r2 = -7r + 7r + 2r2 + -2r2

Combine like terms: -7r + 7r = 0
-17 + 6r + 1r2 = 0 + 2r2 + -2r2
-17 + 6r + 1r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
-17 + 6r + 1r2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + 6r + 17 + r2 = 0 + 17

Reorder the terms:
-17 + 17 + 6r + r2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 6r + r2 = 0 + 17
6r + r2 = 0 + 17

Combine like terms: 0 + 17 = 17
6r + r2 = 17

The r term is 6r.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6r + 9 + r2 = 17 + 9

Reorder the terms:
9 + 6r + r2 = 17 + 9

Combine like terms: 17 + 9 = 26
9 + 6r + r2 = 26

Factor a perfect square on the left side:
(r + 3)(r + 3) = 26

Calculate the square root of the right side: 5.099019514

Break this problem into two subproblems by setting 
(r + 3) equal to 5.099019514 and -5.099019514.

Subproblem 1
r + 3 = 5.099019514

Simplifying
r + 3 = 5.099019514

Reorder the terms:
3 + r = 5.099019514

Solving
3 + r = 5.099019514

Solving for variable 'r'.

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

Add '-3' to each side of the equation.
3 + -3 + r = 5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + r = 5.099019514 + -3
r = 5.099019514 + -3

Combine like terms: 5.099019514 + -3 = 2.099019514
r = 2.099019514

Simplifying
r = 2.099019514

Subproblem 2
r + 3 = -5.099019514

Simplifying
r + 3 = -5.099019514

Reorder the terms:
3 + r = -5.099019514

Solving
3 + r = -5.099019514

Solving for variable 'r'.

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

Add '-3' to each side of the equation.
3 + -3 + r = -5.099019514 + -3

Combine like terms: 3 + -3 = 0
0 + r = -5.099019514 + -3
r = -5.099019514 + -3

Combine like terms: -5.099019514 + -3 = -8.099019514
r = -8.099019514

Simplifying
r = -8.099019514

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {2.099019514, -8.099019514}