q^2+14q=-48

Solution for q^2+14q=-48 equation:

Simplifying
q2 + 14q = -48

Reorder the terms:
14q + q2 = -48

Solving
14q + q2 = -48

Solving for variable 'q'.

Reorder the terms:
48 + 14q + q2 = -48 + 48

Combine like terms: -48 + 48 = 0
48 + 14q + q2 = 0

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

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

Simplifying
8 + q = 0

Solving
8 + q = 0

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

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

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

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

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

Simplifying
6 + q = 0

Solving
6 + q = 0

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

Add '-6' to each side of the equation.
6 + -6 + q = 0 + -6

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

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

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