a^2+4a-72=5

Solution for a^2+4a-72=5 equation:

Simplifying
a2 + 4a + -72 = 5

Reorder the terms:
-72 + 4a + a2 = 5

Solving
-72 + 4a + a2 = 5

Solving for variable 'a'.

Reorder the terms:
-72 + -5 + 4a + a2 = 5 + -5

Combine like terms: -72 + -5 = -77
-77 + 4a + a2 = 5 + -5

Combine like terms: 5 + -5 = 0
-77 + 4a + a2 = 0

Factor a trinomial.
(-11 + -1a)(7 + -1a) = 0

Subproblem 1
Set the factor '(-11 + -1a)' equal to zero and attempt to solve:

Simplifying
-11 + -1a = 0

Solving
-11 + -1a = 0

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

Add '11' to each side of the equation.
-11 + 11 + -1a = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -1a = 0 + 11
-1a = 0 + 11

Combine like terms: 0 + 11 = 11
-1a = 11

Divide each side by '-1'.
a = -11

Simplifying
a = -11
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {-11, 7}