12r^2+r=6

Solution for 12r^2+r=6 equation:

Simplifying
12r2 + r = 6

Reorder the terms:
r + 12r2 = 6

Solving
r + 12r2 = 6

Solving for variable 'r'.

Reorder the terms:
-6 + r + 12r2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + r + 12r2 = 0

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

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

Simplifying
-3 + -4r = 0

Solving
-3 + -4r = 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 + -4r = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4r = 0 + 3
-4r = 0 + 3

Combine like terms: 0 + 3 = 3
-4r = 3

Divide each side by '-4'.
r = -0.75

Simplifying
r = -0.75
Subproblem 2
Set the factor '(2 + -3r)' equal to zero and attempt to solve:

Simplifying
2 + -3r = 0

Solving
2 + -3r = 0

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

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

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

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

Divide each side by '-3'.
r = 0.6666666667

Simplifying
r = 0.6666666667
Solution
r = {-0.75, 0.6666666667}