a^2=17a-72

Solution for a^2=17a-72 equation:

Simplifying
a2 = 17a + -72

Reorder the terms:
a2 = -72 + 17a

Solving
a2 = -72 + 17a

Solving for variable 'a'.

Reorder the terms:
72 + -17a + a2 = -72 + 17a + 72 + -17a

Reorder the terms:
72 + -17a + a2 = -72 + 72 + 17a + -17a

Combine like terms: -72 + 72 = 0
72 + -17a + a2 = 0 + 17a + -17a
72 + -17a + a2 = 17a + -17a

Combine like terms: 17a + -17a = 0
72 + -17a + a2 = 0

Factor a trinomial.
(8 + -1a)(9 + -1a) = 0

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

Simplifying
8 + -1a = 0

Solving
8 + -1a = 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 + -1a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1a = 0 + -8
-1a = 0 + -8

Combine like terms: 0 + -8 = -8
-1a = -8

Divide each side by '-1'.
a = 8

Simplifying
a = 8
Subproblem 2
Set the factor '(9 + -1a)' equal to zero and attempt to solve:

Simplifying
9 + -1a = 0

Solving
9 + -1a = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1a = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1a = 0 + -9
-1a = 0 + -9

Combine like terms: 0 + -9 = -9
-1a = -9

Divide each side by '-1'.
a = 9

Simplifying
a = 9
Solution
a = {8, 9}