0=a^2+14a-576

Solution for 0=a^2+14a-576 equation:

Simplifying
0 = a2 + 14a + -576

Reorder the terms:
0 = -576 + 14a + a2

Solving
0 = -576 + 14a + a2

Solving for variable 'a'.

Combine like terms: 0 + 576 = 576
576 + -14a + -1a2 = -576 + 14a + a2 + 576 + -14a + -1a2

Reorder the terms:
576 + -14a + -1a2 = -576 + 576 + 14a + -14a + a2 + -1a2

Combine like terms: -576 + 576 = 0
576 + -14a + -1a2 = 0 + 14a + -14a + a2 + -1a2
576 + -14a + -1a2 = 14a + -14a + a2 + -1a2

Combine like terms: 14a + -14a = 0
576 + -14a + -1a2 = 0 + a2 + -1a2
576 + -14a + -1a2 = a2 + -1a2

Combine like terms: a2 + -1a2 = 0
576 + -14a + -1a2 = 0

Factor a trinomial.
(18 + -1a)(32 + a) = 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 '(32 + a)' equal to zero and attempt to solve:

Simplifying
32 + a = 0

Solving
32 + a = 0

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

Add '-32' to each side of the equation.
32 + -32 + a = 0 + -32

Combine like terms: 32 + -32 = 0
0 + a = 0 + -32
a = 0 + -32

Combine like terms: 0 + -32 = -32
a = -32

Simplifying
a = -32
Solution
a = {18, -32}