r=-1+6r^2

Solution for r=-1+6r^2 equation:

Simplifying
r = -1 + 6r2

Solving
r = -1 + 6r2

Solving for variable 'r'.

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

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

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

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

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

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 '(1 + 3r)' equal to zero and attempt to solve:

Simplifying
1 + 3r = 0

Solving
1 + 3r = 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 + 3r = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3r = 0 + -1
3r = 0 + -1

Combine like terms: 0 + -1 = -1
3r = -1

Divide each side by '3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Solution
r = {0.5, -0.3333333333}