12r^2-38r-16=0

Solution for 12r^2-38r-16=0 equation:

Simplifying
12r2 + -38r + -16 = 0

Reorder the terms:
-16 + -38r + 12r2 = 0

Solving
-16 + -38r + 12r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -19r + 6r2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + -19r + 6r2)' equal to zero and attempt to solve:

Simplifying
-8 + -19r + 6r2 = 0

Solving
-8 + -19r + 6r2 = 0

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

Divide each side by '6'.
-1.333333333 + -3.166666667r + r2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + -3.166666667r + 1.333333333 + r2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + -3.166666667r + r2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + -3.166666667r + r2 = 0 + 1.333333333
-3.166666667r + r2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
-3.166666667r + r2 = 1.333333333

The r term is -3.166666667r.  Take half its coefficient (-1.583333334).
Square it (2.506944447) and add it to both sides.

Add '2.506944447' to each side of the equation.
-3.166666667r + 2.506944447 + r2 = 1.333333333 + 2.506944447

Reorder the terms:
2.506944447 + -3.166666667r + r2 = 1.333333333 + 2.506944447

Combine like terms: 1.333333333 + 2.506944447 = 3.84027778
2.506944447 + -3.166666667r + r2 = 3.84027778

Factor a perfect square on the left side:
(r + -1.583333334)(r + -1.583333334) = 3.84027778

Calculate the square root of the right side: 1.95966267

Break this problem into two subproblems by setting 
(r + -1.583333334) equal to 1.95966267 and -1.95966267.

Subproblem 1
r + -1.583333334 = 1.95966267

Simplifying
r + -1.583333334 = 1.95966267

Reorder the terms:
-1.583333334 + r = 1.95966267

Solving
-1.583333334 + r = 1.95966267

Solving for variable 'r'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + r = 1.95966267 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + r = 1.95966267 + 1.583333334
r = 1.95966267 + 1.583333334

Combine like terms: 1.95966267 + 1.583333334 = 3.542996004
r = 3.542996004

Simplifying
r = 3.542996004

Subproblem 2
r + -1.583333334 = -1.95966267

Simplifying
r + -1.583333334 = -1.95966267

Reorder the terms:
-1.583333334 + r = -1.95966267

Solving
-1.583333334 + r = -1.95966267

Solving for variable 'r'.

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

Add '1.583333334' to each side of the equation.
-1.583333334 + 1.583333334 + r = -1.95966267 + 1.583333334

Combine like terms: -1.583333334 + 1.583333334 = 0.000000000
0.000000000 + r = -1.95966267 + 1.583333334
r = -1.95966267 + 1.583333334

Combine like terms: -1.95966267 + 1.583333334 = -0.376329336
r = -0.376329336

Simplifying
r = -0.376329336

Solution
The solution to the problem is based on the solutions
from the subproblems.
r = {3.542996004, -0.376329336}
Solution
r = {3.542996004, -0.376329336}