a^2+14a+48=0

Solution for a^2+14a+48=0 equation:

Simplifying
a2 + 14a + 48 = 0

Reorder the terms:
48 + 14a + a2 = 0

Solving
48 + 14a + a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(8 + a)(6 + a) = 0

Subproblem 1
Set the factor '(8 + a)' equal to zero and attempt to solve:

Simplifying
8 + a = 0

Solving
8 + a = 0

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

Add '-8' to each side of the equation.
8 + -8 + a = 0 + -8

Combine like terms: 8 + -8 = 0
0 + a = 0 + -8
a = 0 + -8

Combine like terms: 0 + -8 = -8
a = -8

Simplifying
a = -8
Subproblem 2
Set the factor '(6 + a)' equal to zero and attempt to solve:

Simplifying
6 + a = 0

Solving
6 + a = 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 + a = 0 + -6

Combine like terms: 6 + -6 = 0
0 + a = 0 + -6
a = 0 + -6

Combine like terms: 0 + -6 = -6
a = -6

Simplifying
a = -6
Solution
a = {-8, -6}