3r^2-39r+90=0

Solution for 3r^2-39r+90=0 equation:

Simplifying
3r2 + -39r + 90 = 0

Reorder the terms:
90 + -39r + 3r2 = 0

Solving
90 + -39r + 3r2 = 0

Solving for variable 'r'.

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -13r + r2) = 0

Factor a trinomial.
3((3 + -1r)(10 + -1r)) = 0

Ignore the factor 3.
Subproblem 1
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
Subproblem 2
Set the factor '(10 + -1r)' equal to zero and attempt to solve:

Simplifying
10 + -1r = 0

Solving
10 + -1r = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1r = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1r = 0 + -10
-1r = 0 + -10

Combine like terms: 0 + -10 = -10
-1r = -10

Divide each side by '-1'.
r = 10

Simplifying
r = 10
Solution
r = {3, 10}