16r^2-16r-12=0

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

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

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

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

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + -4r + 4r2) = 0

Factor a trinomial.
4((-1 + -2r)(3 + -2r)) = 0

Ignore the factor 4.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -2r)' equal to zero and attempt to solve:

Simplifying
3 + -2r = 0

Solving
3 + -2r = 0

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

Add '-3' to each side of the equation.
3 + -3 + -2r = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2r = 0 + -3
-2r = 0 + -3

Combine like terms: 0 + -3 = -3
-2r = -3

Divide each side by '-2'.
r = 1.5

Simplifying
r = 1.5
Solution
r = {-0.5, 1.5}