6r^2+r=1

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

Simplifying
6r2 + r = 1

Reorder the terms:
r + 6r2 = 1

Solving
r + 6r2 = 1

Solving for variable 'r'.

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

Combine like terms: 1 + -1 = 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}