3a^2-27a+60=0

Solution for 3a^2-27a+60=0 equation:

Simplifying
3a2 + -27a + 60 = 0

Reorder the terms:
60 + -27a + 3a2 = 0

Solving
60 + -27a + 3a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -9a + a2) = 0

Factor a trinomial.
3((4 + -1a)(5 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -1a)' equal to zero and attempt to solve:

Simplifying
4 + -1a = 0

Solving
4 + -1a = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1a = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1a = 0 + -4
-1a = 0 + -4

Combine like terms: 0 + -4 = -4
-1a = -4

Divide each side by '-1'.
a = 4

Simplifying
a = 4
Subproblem 2
Set the factor '(5 + -1a)' equal to zero and attempt to solve:

Simplifying
5 + -1a = 0

Solving
5 + -1a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1a = 0 + -5

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

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

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

Simplifying
a = 5
Solution
a = {4, 5}