9a^2-51a+72=0

Solution for 9a^2-51a+72=0 equation:

Simplifying
9a2 + -51a + 72 = 0

Reorder the terms:
72 + -51a + 9a2 = 0

Solving
72 + -51a + 9a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + -17a + 3a2) = 0

Factor a trinomial.
3((8 + -3a)(3 + -1a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(8 + -3a)' equal to zero and attempt to solve:

Simplifying
8 + -3a = 0

Solving
8 + -3a = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3a = 0 + -8
-3a = 0 + -8

Combine like terms: 0 + -8 = -8
-3a = -8

Divide each side by '-3'.
a = 2.666666667

Simplifying
a = 2.666666667
Subproblem 2
Set the factor '(3 + -1a)' equal to zero and attempt to solve:

Simplifying
3 + -1a = 0

Solving
3 + -1a = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1a = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1a = 0 + -3
-1a = 0 + -3

Combine like terms: 0 + -3 = -3
-1a = -3

Divide each side by '-1'.
a = 3

Simplifying
a = 3
Solution
a = {2.666666667, 3}