a^2+14a-72=0

Solution for a^2+14a-72=0 equation:

Simplifying
a2 + 14a + -72 = 0

Reorder the terms:
-72 + 14a + a2 = 0

Solving
-72 + 14a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-18 + -1a)(4 + -1a) = 0

Subproblem 1
Set the factor '(-18 + -1a)' equal to zero and attempt to solve:

Simplifying
-18 + -1a = 0

Solving
-18 + -1a = 0

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

Add '18' to each side of the equation.
-18 + 18 + -1a = 0 + 18

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

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

Divide each side by '-1'.
a = -18

Simplifying
a = -18
Subproblem 2
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
Solution
a = {-18, 4}