-6(2r+8)=-10r(r-3)

Solution for -6(2r+8)=-10r(r-3) equation:

Simplifying
-6(2r + 8) = -10r(r + -3)

Reorder the terms:
-6(8 + 2r) = -10r(r + -3)
(8 * -6 + 2r * -6) = -10r(r + -3)
(-48 + -12r) = -10r(r + -3)

Reorder the terms:
-48 + -12r = -10r(-3 + r)
-48 + -12r = (-3 * -10r + r * -10r)
-48 + -12r = (30r + -10r2)

Solving
-48 + -12r = 30r + -10r2

Solving for variable 'r'.

Combine like terms: -12r + -30r = -42r
-48 + -42r + 10r2 = 30r + -10r2 + -30r + 10r2

Reorder the terms:
-48 + -42r + 10r2 = 30r + -30r + -10r2 + 10r2

Combine like terms: 30r + -30r = 0
-48 + -42r + 10r2 = 0 + -10r2 + 10r2
-48 + -42r + 10r2 = -10r2 + 10r2

Combine like terms: -10r2 + 10r2 = 0
-48 + -42r + 10r2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + -21r + 5r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-24 + -21r + 5r2)' equal to zero and attempt to solve:

Simplifying
-24 + -21r + 5r2 = 0

Solving
-24 + -21r + 5r2 = 0

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

Divide each side by '5'.
-4.8 + -4.2r + r2 = 0

Move the constant term to the right:

Add '4.8' to each side of the equation.
-4.8 + -4.2r + 4.8 + r2 = 0 + 4.8

Reorder the terms:
-4.8 + 4.8 + -4.2r + r2 = 0 + 4.8

Combine like terms: -4.8 + 4.8 = 0.0
0.0 + -4.2r + r2 = 0 + 4.8
-4.2r + r2 = 0 + 4.8

Combine like terms: 0 + 4.8 = 4.8
-4.2r + r2 = 4.8

The r term is -4.2r.  Take half its coefficient (-2.1).
Square it (4.41) and add it to both sides.

Add '4.41' to each side of the equation.
-4.2r + 4.41 + r2 = 4.8 + 4.41

Reorder the terms:
4.41 + -4.2r + r2 = 4.8 + 4.41

Combine like terms: 4.8 + 4.41 = 9.21
4.41 + -4.2r + r2 = 9.21

Factor a perfect square on the left side:
(r + -2.1)(r + -2.1) = 9.21

Calculate the square root of the right side: 3.034798181

Break this problem into two subproblems by setting 
(r + -2.1) equal to 3.034798181 and -3.034798181.

Subproblem 1
r + -2.1 = 3.034798181

Simplifying
r + -2.1 = 3.034798181

Reorder the terms:
-2.1 + r = 3.034798181

Solving
-2.1 + r = 3.034798181

Solving for variable 'r'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + r = 3.034798181 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + r = 3.034798181 + 2.1
r = 3.034798181 + 2.1

Combine like terms: 3.034798181 + 2.1 = 5.134798181
r = 5.134798181

Simplifying
r = 5.134798181

Subproblem 2
r + -2.1 = -3.034798181

Simplifying
r + -2.1 = -3.034798181

Reorder the terms:
-2.1 + r = -3.034798181

Solving
-2.1 + r = -3.034798181

Solving for variable 'r'.

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

Add '2.1' to each side of the equation.
-2.1 + 2.1 + r = -3.034798181 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + r = -3.034798181 + 2.1
r = -3.034798181 + 2.1

Combine like terms: -3.034798181 + 2.1 = -0.934798181
r = -0.934798181

Simplifying
r = -0.934798181

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {5.134798181, -0.934798181}
Solution
r = {5.134798181, -0.934798181}