6r^2-3r=3

Solution for 6r^2-3r=3 equation:

Simplifying
6r2 + -3r = 3

Reorder the terms:
-3r + 6r2 = 3

Solving
-3r + 6r2 = 3

Solving for variable 'r'.

Reorder the terms:
-3 + -3r + 6r2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -3r + 6r2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -1r + 2r2) = 0

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

Ignore the factor 3.
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 + -1r)' equal to zero and attempt to solve:

Simplifying
1 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 1

Simplifying
r = 1
Solution
r = {-0.5, 1}