x^2+16x+51=-4

Solution for x^2+16x+51=-4 equation:

Simplifying
x2 + 16x + 51 = -4

Reorder the terms:
51 + 16x + x2 = -4

Solving
51 + 16x + x2 = -4

Solving for variable 'x'.

Reorder the terms:
51 + 4 + 16x + x2 = -4 + 4

Combine like terms: 51 + 4 = 55
55 + 16x + x2 = -4 + 4

Combine like terms: -4 + 4 = 0
55 + 16x + x2 = 0

Factor a trinomial.
(11 + x)(5 + x) = 0

Subproblem 1
Set the factor '(11 + x)' equal to zero and attempt to solve:

Simplifying
11 + x = 0

Solving
11 + x = 0

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

Add '-11' to each side of the equation.
11 + -11 + x = 0 + -11

Combine like terms: 11 + -11 = 0
0 + x = 0 + -11
x = 0 + -11

Combine like terms: 0 + -11 = -11
x = -11

Simplifying
x = -11
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-11, -5}