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.
(-1 + -3r)(2 + -1r) = 0

Subproblem 1
Set the factor '(-1 + -3r)' equal to zero and attempt to solve:

Simplifying
-1 + -3r = 0

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

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

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

Divide each side by '-3'.
r = -0.3333333333

Simplifying
r = -0.3333333333
Subproblem 2
Set the factor '(2 + -1r)' equal to zero and attempt to solve:

Simplifying
2 + -1r = 0

Solving
2 + -1r = 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 + -1r = 0 + -2

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

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

Divide each side by '-1'.
r = 2

Simplifying
r = 2
Solution
r = {-0.3333333333, 2}