9a^2-66a+90=3a

Solution for 9a^2-66a+90=3a equation:

Simplifying
9a2 + -66a + 90 = 3a

Reorder the terms:
90 + -66a + 9a2 = 3a

Solving
90 + -66a + 9a2 = 3a

Solving for variable 'a'.

Reorder the terms:
90 + -66a + -3a + 9a2 = 3a + -3a

Combine like terms: -66a + -3a = -69a
90 + -69a + 9a2 = 3a + -3a

Combine like terms: 3a + -3a = 0
90 + -69a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(30 + -23a + 3a2) = 0

Factor a trinomial.
3((5 + -3a)(6 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

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

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

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

Simplifying
a = 1.666666667
Subproblem 2
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1a = 0 + -6
-1a = 0 + -6

Combine like terms: 0 + -6 = -6
-1a = -6

Divide each side by '-1'.
a = 6

Simplifying
a = 6
Solution
a = {1.666666667, 6}