r(6r+1)=12

Solution for r(6r+1)=12 equation:

Simplifying
r(6r + 1) = 12

Reorder the terms:
r(1 + 6r) = 12
(1 * r + 6r * r) = 12
(1r + 6r2) = 12

Solving
1r + 6r2 = 12

Solving for variable 'r'.

Reorder the terms:
-12 + 1r + 6r2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 1r + 6r2 = 0

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

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

Simplifying
4 + -3r = 0

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

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

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

Divide each side by '-3'.
r = 1.333333333

Simplifying
r = 1.333333333
Solution
r = {-1.5, 1.333333333}