9a^2-52a+64=0

Solution for 9a^2-52a+64=0 equation:

Simplifying
9a2 + -52a + 64 = 0

Reorder the terms:
64 + -52a + 9a2 = 0

Solving
64 + -52a + 9a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(16 + -9a)(4 + -1a) = 0

Subproblem 1
Set the factor '(16 + -9a)' equal to zero and attempt to solve:

Simplifying
16 + -9a = 0

Solving
16 + -9a = 0

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

Add '-16' to each side of the equation.
16 + -16 + -9a = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -9a = 0 + -16
-9a = 0 + -16

Combine like terms: 0 + -16 = -16
-9a = -16

Divide each side by '-9'.
a = 1.777777778

Simplifying
a = 1.777777778
Subproblem 2
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
Solution
a = {1.777777778, 4}