5(r-1)=2r(r-4)-6

Solution for 5(r-1)=2r(r-4)-6 equation:

Simplifying
5(r + -1) = 2r(r + -4) + -6

Reorder the terms:
5(-1 + r) = 2r(r + -4) + -6
(-1 * 5 + r * 5) = 2r(r + -4) + -6
(-5 + 5r) = 2r(r + -4) + -6

Reorder the terms:
-5 + 5r = 2r(-4 + r) + -6
-5 + 5r = (-4 * 2r + r * 2r) + -6
-5 + 5r = (-8r + 2r2) + -6

Reorder the terms:
-5 + 5r = -6 + -8r + 2r2

Solving
-5 + 5r = -6 + -8r + 2r2

Solving for variable 'r'.

Reorder the terms:
-5 + 6 + 5r + 8r + -2r2 = -6 + -8r + 2r2 + 6 + 8r + -2r2

Combine like terms: -5 + 6 = 1
1 + 5r + 8r + -2r2 = -6 + -8r + 2r2 + 6 + 8r + -2r2

Combine like terms: 5r + 8r = 13r
1 + 13r + -2r2 = -6 + -8r + 2r2 + 6 + 8r + -2r2

Reorder the terms:
1 + 13r + -2r2 = -6 + 6 + -8r + 8r + 2r2 + -2r2

Combine like terms: -6 + 6 = 0
1 + 13r + -2r2 = 0 + -8r + 8r + 2r2 + -2r2
1 + 13r + -2r2 = -8r + 8r + 2r2 + -2r2

Combine like terms: -8r + 8r = 0
1 + 13r + -2r2 = 0 + 2r2 + -2r2
1 + 13r + -2r2 = 2r2 + -2r2

Combine like terms: 2r2 + -2r2 = 0
1 + 13r + -2r2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-0.5 + -6.5r + r2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -6.5r + 0.5 + r2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -6.5r + r2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -6.5r + r2 = 0 + 0.5
-6.5r + r2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-6.5r + r2 = 0.5

The r term is -6.5r.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5r + 10.5625 + r2 = 0.5 + 10.5625

Reorder the terms:
10.5625 + -6.5r + r2 = 0.5 + 10.5625

Combine like terms: 0.5 + 10.5625 = 11.0625
10.5625 + -6.5r + r2 = 11.0625

Factor a perfect square on the left side:
(r + -3.25)(r + -3.25) = 11.0625

Calculate the square root of the right side: 3.326033674

Break this problem into two subproblems by setting 
(r + -3.25) equal to 3.326033674 and -3.326033674.

Subproblem 1
r + -3.25 = 3.326033674

Simplifying
r + -3.25 = 3.326033674

Reorder the terms:
-3.25 + r = 3.326033674

Solving
-3.25 + r = 3.326033674

Solving for variable 'r'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + r = 3.326033674 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + r = 3.326033674 + 3.25
r = 3.326033674 + 3.25

Combine like terms: 3.326033674 + 3.25 = 6.576033674
r = 6.576033674

Simplifying
r = 6.576033674

Subproblem 2
r + -3.25 = -3.326033674

Simplifying
r + -3.25 = -3.326033674

Reorder the terms:
-3.25 + r = -3.326033674

Solving
-3.25 + r = -3.326033674

Solving for variable 'r'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + r = -3.326033674 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + r = -3.326033674 + 3.25
r = -3.326033674 + 3.25

Combine like terms: -3.326033674 + 3.25 = -0.076033674
r = -0.076033674

Simplifying
r = -0.076033674

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {6.576033674, -0.076033674}