a^2-22a+72=0

Solution for a^2-22a+72=0 equation:

Simplifying
a2 + -22a + 72 = 0

Reorder the terms:
72 + -22a + a2 = 0

Solving
72 + -22a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4 + -1a)(18 + -1a) = 0

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 '(18 + -1a)' equal to zero and attempt to solve:

Simplifying
18 + -1a = 0

Solving
18 + -1a = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1a = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1a = 0 + -18
-1a = 0 + -18

Combine like terms: 0 + -18 = -18
-1a = -18

Divide each side by '-1'.
a = 18

Simplifying
a = 18
Solution
a = {4, 18}