6a^2-60a+150=0

Solution for 6a^2-60a+150=0 equation:

Simplifying
6a2 + -60a + 150 = 0

Reorder the terms:
150 + -60a + 6a2 = 0

Solving
150 + -60a + 6a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(25 + -10a + a2) = 0

Factor a trinomial.
6((5 + -1a)(5 + -1a)) = 0

Ignore the factor 6.
Subproblem 1
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
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 = {5, 5}