66r^2+57r+12=0

Solution for 66r^2+57r+12=0 equation:

Simplifying
66r2 + 57r + 12 = 0

Reorder the terms:
12 + 57r + 66r2 = 0

Solving
12 + 57r + 66r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4 + 19r + 22r2) = 0

Factor a trinomial.
3((1 + 2r)(4 + 11r)) = 0

Ignore the factor 3.
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 '(4 + 11r)' equal to zero and attempt to solve:

Simplifying
4 + 11r = 0

Solving
4 + 11r = 0

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

Add '-4' to each side of the equation.
4 + -4 + 11r = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 11r = 0 + -4
11r = 0 + -4

Combine like terms: 0 + -4 = -4
11r = -4

Divide each side by '11'.
r = -0.3636363636

Simplifying
r = -0.3636363636
Solution
r = {-0.5, -0.3636363636}