3r^2=5r-2

Solution for 3r^2=5r-2 equation:

Simplifying
3r2 = 5r + -2

Reorder the terms:
3r2 = -2 + 5r

Solving
3r2 = -2 + 5r

Solving for variable 'r'.

Reorder the terms:
2 + -5r + 3r2 = -2 + 5r + 2 + -5r

Reorder the terms:
2 + -5r + 3r2 = -2 + 2 + 5r + -5r

Combine like terms: -2 + 2 = 0
2 + -5r + 3r2 = 0 + 5r + -5r
2 + -5r + 3r2 = 5r + -5r

Combine like terms: 5r + -5r = 0
2 + -5r + 3r2 = 0

Factor a trinomial.
(2 + -3r)(1 + -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 '(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 = {0.6666666667, 1}