6r^2-13r+3=-3

Solution for 6r^2-13r+3=-3 equation:

Simplifying
6r2 + -13r + 3 = -3

Reorder the terms:
3 + -13r + 6r2 = -3

Solving
3 + -13r + 6r2 = -3

Solving for variable 'r'.

Reorder the terms:
3 + 3 + -13r + 6r2 = -3 + 3

Combine like terms: 3 + 3 = 6
6 + -13r + 6r2 = -3 + 3

Combine like terms: -3 + 3 = 0
6 + -13r + 6r2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
r = {0.6666666667, 1.5}