3r^2=2r+5

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

Simplifying
3r2 = 2r + 5

Reorder the terms:
3r2 = 5 + 2r

Solving
3r2 = 5 + 2r

Solving for variable 'r'.

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

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

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

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

Factor a trinomial.
(-1 + -1r)(5 + -3r) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -3r)' equal to zero and attempt to solve:

Simplifying
5 + -3r = 0

Solving
5 + -3r = 0

Move all terms containing r to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -3r = 0 + -5

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

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

Divide each side by '-3'.
r = 1.666666667

Simplifying
r = 1.666666667
Solution
r = {-1, 1.666666667}