3r^2-65=-2r

Solution for 3r^2-65=-2r equation:

Simplifying
3r2 + -65 = -2r

Reorder the terms:
-65 + 3r2 = -2r

Solving
-65 + 3r2 = -2r

Solving for variable 'r'.

Reorder the terms:
-65 + 2r + 3r2 = -2r + 2r

Combine like terms: -2r + 2r = 0
-65 + 2r + 3r2 = 0

Factor a trinomial.
(-5 + -1r)(13 + -3r) = 0

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

Simplifying
-5 + -1r = 0

Solving
-5 + -1r = 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 + -1r = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1r = 0 + 5
-1r = 0 + 5

Combine like terms: 0 + 5 = 5
-1r = 5

Divide each side by '-1'.
r = -5

Simplifying
r = -5
Subproblem 2
Set the factor '(13 + -3r)' equal to zero and attempt to solve:

Simplifying
13 + -3r = 0

Solving
13 + -3r = 0

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

Add '-13' to each side of the equation.
13 + -13 + -3r = 0 + -13

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

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

Divide each side by '-3'.
r = 4.333333333

Simplifying
r = 4.333333333
Solution
r = {-5, 4.333333333}