-8r(3r+6)-4(r-7)=

Solution for -8r(3r+6)-4(r-7)= equation:

Simplifying
-8r(3r + 6) + -4(r + -7) = 0

Reorder the terms:
-8r(6 + 3r) + -4(r + -7) = 0
(6 * -8r + 3r * -8r) + -4(r + -7) = 0
(-48r + -24r2) + -4(r + -7) = 0

Reorder the terms:
-48r + -24r2 + -4(-7 + r) = 0
-48r + -24r2 + (-7 * -4 + r * -4) = 0
-48r + -24r2 + (28 + -4r) = 0

Reorder the terms:
28 + -48r + -4r + -24r2 = 0

Combine like terms: -48r + -4r = -52r
28 + -52r + -24r2 = 0

Solving
28 + -52r + -24r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(7 + -13r + -6r2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(7 + -13r + -6r2)' equal to zero and attempt to solve:

Simplifying
7 + -13r + -6r2 = 0

Solving
7 + -13r + -6r2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1.166666667 + 2.166666667r + r2 = 0

Move the constant term to the right:

Add '1.166666667' to each side of the equation.
-1.166666667 + 2.166666667r + 1.166666667 + r2 = 0 + 1.166666667

Reorder the terms:
-1.166666667 + 1.166666667 + 2.166666667r + r2 = 0 + 1.166666667

Combine like terms: -1.166666667 + 1.166666667 = 0.000000000
0.000000000 + 2.166666667r + r2 = 0 + 1.166666667
2.166666667r + r2 = 0 + 1.166666667

Combine like terms: 0 + 1.166666667 = 1.166666667
2.166666667r + r2 = 1.166666667

The r term is 2.166666667r.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667r + 1.173611113 + r2 = 1.166666667 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667r + r2 = 1.166666667 + 1.173611113

Combine like terms: 1.166666667 + 1.173611113 = 2.34027778
1.173611113 + 2.166666667r + r2 = 2.34027778

Factor a perfect square on the left side:
(r + 1.083333334)(r + 1.083333334) = 2.34027778

Calculate the square root of the right side: 1.529796647

Break this problem into two subproblems by setting 
(r + 1.083333334) equal to 1.529796647 and -1.529796647.

Subproblem 1
r + 1.083333334 = 1.529796647

Simplifying
r + 1.083333334 = 1.529796647

Reorder the terms:
1.083333334 + r = 1.529796647

Solving
1.083333334 + r = 1.529796647

Solving for variable 'r'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + r = 1.529796647 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + r = 1.529796647 + -1.083333334
r = 1.529796647 + -1.083333334

Combine like terms: 1.529796647 + -1.083333334 = 0.446463313
r = 0.446463313

Simplifying
r = 0.446463313

Subproblem 2
r + 1.083333334 = -1.529796647

Simplifying
r + 1.083333334 = -1.529796647

Reorder the terms:
1.083333334 + r = -1.529796647

Solving
1.083333334 + r = -1.529796647

Solving for variable 'r'.

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

Add '-1.083333334' to each side of the equation.
1.083333334 + -1.083333334 + r = -1.529796647 + -1.083333334

Combine like terms: 1.083333334 + -1.083333334 = 0.000000000
0.000000000 + r = -1.529796647 + -1.083333334
r = -1.529796647 + -1.083333334

Combine like terms: -1.529796647 + -1.083333334 = -2.613129981
r = -2.613129981

Simplifying
r = -2.613129981

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {0.446463313, -2.613129981}
Solution
r = {0.446463313, -2.613129981}