-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

Factor a trinomial.
2((-8 + 3r)(1 + -2r)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-8 + 3r)' equal to zero and attempt to solve:

Simplifying
-8 + 3r = 0

Solving
-8 + 3r = 0

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

Add '8' to each side of the equation.
-8 + 8 + 3r = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 3r = 0 + 8
3r = 0 + 8

Combine like terms: 0 + 8 = 8
3r = 8

Divide each side by '3'.
r = 2.666666667

Simplifying
r = 2.666666667
Subproblem 2
Set the factor '(1 + -2r)' equal to zero and attempt to solve:

Simplifying
1 + -2r = 0

Solving
1 + -2r = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2r = 0 + -1

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

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

Divide each side by '-2'.
r = 0.5

Simplifying
r = 0.5
Solution
r = {2.666666667, 0.5}