3r^2=-6+11r

Solution for 3r^2=-6+11r equation:

Simplifying
3r2 = -6 + 11r

Solving
3r2 = -6 + 11r

Solving for variable 'r'.

Reorder the terms:
6 + -11r + 3r2 = -6 + 11r + 6 + -11r

Reorder the terms:
6 + -11r + 3r2 = -6 + 6 + 11r + -11r

Combine like terms: -6 + 6 = 0
6 + -11r + 3r2 = 0 + 11r + -11r
6 + -11r + 3r2 = 11r + -11r

Combine like terms: 11r + -11r = 0
6 + -11r + 3r2 = 0

Factor a trinomial.
(2 + -3r)(3 + -1r) = 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 + -1r)' equal to zero and attempt to solve:

Simplifying
3 + -1r = 0

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

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

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

Divide each side by '-1'.
r = 3

Simplifying
r = 3
Solution
r = {0.6666666667, 3}