0=a^2-18a+72

Solution for 0=a^2-18a+72 equation:

Simplifying
0 = a2 + -18a + 72

Reorder the terms:
0 = 72 + -18a + a2

Solving
0 = 72 + -18a + a2

Solving for variable 'a'.

Combine like terms: 0 + -72 = -72
-72 + 18a + -1a2 = 72 + -18a + a2 + -72 + 18a + -1a2

Reorder the terms:
-72 + 18a + -1a2 = 72 + -72 + -18a + 18a + a2 + -1a2

Combine like terms: 72 + -72 = 0
-72 + 18a + -1a2 = 0 + -18a + 18a + a2 + -1a2
-72 + 18a + -1a2 = -18a + 18a + a2 + -1a2

Combine like terms: -18a + 18a = 0
-72 + 18a + -1a2 = 0 + a2 + -1a2
-72 + 18a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
-72 + 18a + -1a2 = 0

Factor a trinomial.
(-12 + a)(6 + -1a) = 0

Subproblem 1
Set the factor '(-12 + a)' equal to zero and attempt to solve:

Simplifying
-12 + a = 0

Solving
-12 + a = 0

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

Add '12' to each side of the equation.
-12 + 12 + a = 0 + 12

Combine like terms: -12 + 12 = 0
0 + a = 0 + 12
a = 0 + 12

Combine like terms: 0 + 12 = 12
a = 12

Simplifying
a = 12
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 = {12, 6}