0=12r^2+38r-16

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

Simplifying
0 = 12r2 + 38r + -16

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

Solving
0 = -16 + 38r + 12r2

Solving for variable 'r'.

Combine like terms: 0 + 16 = 16
16 + -38r + -12r2 = -16 + 38r + 12r2 + 16 + -38r + -12r2

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

Combine like terms: -16 + 16 = 0
16 + -38r + -12r2 = 0 + 38r + -38r + 12r2 + -12r2
16 + -38r + -12r2 = 38r + -38r + 12r2 + -12r2

Combine like terms: 38r + -38r = 0
16 + -38r + -12r2 = 0 + 12r2 + -12r2
16 + -38r + -12r2 = 12r2 + -12r2

Combine like terms: 12r2 + -12r2 = 0
16 + -38r + -12r2 = 0

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 = 0.376329336
r = 0.376329336

Simplifying
r = 0.376329336

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 = -3.542996004
r = -3.542996004

Simplifying
r = -3.542996004

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