3r^2-2r-1=0-1

Solution for 3r^2-2r-1=0-1 equation:

Simplifying
3r2 + -2r + -1 = 0 + -1

Reorder the terms:
-1 + -2r + 3r2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1 + -2r + 3r2 = -1

Add '1' to each side of the equation.
-1 + -2r + 1 + 3r2 = -1 + 1

Reorder the terms:
-1 + 1 + -2r + 3r2 = -1 + 1

Combine like terms: -1 + 1 = 0
0 + -2r + 3r2 = -1 + 1
-2r + 3r2 = -1 + 1

Combine like terms: -1 + 1 = 0
-2r + 3r2 = 0

Solving
-2r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), 'r'.
r(-2 + 3r) = 0

Subproblem 1
Set the factor 'r' equal to zero and attempt to solve:

Simplifying
r = 0

Solving
r = 0

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

Simplifying
r = 0
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, 0.6666666667}