(a*a)+6a-72=0

Solution for (a*a)+6a-72=0 equation:

Simplifying
(a * a) + 6a + -72 = 0

Multiply a * a
(a2) + 6a + -72 = 0
a2 + 6a + -72 = 0

Reorder the terms:
-72 + 6a + a2 = 0

Solving
-72 + 6a + a2 = 0

Solving for variable 'a'.

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

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

Simplifying
-12 + -1a = 0

Solving
-12 + -1a = 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 + -1a = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1a = 0 + 12
-1a = 0 + 12

Combine like terms: 0 + 12 = 12
-1a = 12

Divide each side by '-1'.
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}