72=a^2+9a+20

Solution for 72=a^2+9a+20 equation:

Simplifying
72 = a2 + 9a + 20

Reorder the terms:
72 = 20 + 9a + a2

Solving
72 = 20 + 9a + a2

Solving for variable 'a'.

Combine like terms: 72 + -20 = 52
52 + -9a + -1a2 = 20 + 9a + a2 + -20 + -9a + -1a2

Reorder the terms:
52 + -9a + -1a2 = 20 + -20 + 9a + -9a + a2 + -1a2

Combine like terms: 20 + -20 = 0
52 + -9a + -1a2 = 0 + 9a + -9a + a2 + -1a2
52 + -9a + -1a2 = 9a + -9a + a2 + -1a2

Combine like terms: 9a + -9a = 0
52 + -9a + -1a2 = 0 + a2 + -1a2
52 + -9a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
52 + -9a + -1a2 = 0

Factor a trinomial.
(4 + -1a)(13 + a) = 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 '(13 + a)' equal to zero and attempt to solve:

Simplifying
13 + a = 0

Solving
13 + a = 0

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

Add '-13' to each side of the equation.
13 + -13 + a = 0 + -13

Combine like terms: 13 + -13 = 0
0 + a = 0 + -13
a = 0 + -13

Combine like terms: 0 + -13 = -13
a = -13

Simplifying
a = -13
Solution
a = {4, -13}