x^2=-14x-48

Solution for x^2=-14x-48 equation:

Simplifying
x2 = -14x + -48

Reorder the terms:
x2 = -48 + -14x

Solving
x2 = -48 + -14x

Solving for variable 'x'.

Reorder the terms:
48 + 14x + x2 = -48 + -14x + 48 + 14x

Reorder the terms:
48 + 14x + x2 = -48 + 48 + -14x + 14x

Combine like terms: -48 + 48 = 0
48 + 14x + x2 = 0 + -14x + 14x
48 + 14x + x2 = -14x + 14x

Combine like terms: -14x + 14x = 0
48 + 14x + x2 = 0

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

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

Simplifying
8 + x = 0

Solving
8 + x = 0

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

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

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

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

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

Simplifying
6 + x = 0

Solving
6 + x = 0

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

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

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

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

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