x^2+8x+1=-6

Solution for x^2+8x+1=-6 equation:

Simplifying
x2 + 8x + 1 = -6

Reorder the terms:
1 + 8x + x2 = -6

Solving
1 + 8x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
1 + 6 + 8x + x2 = -6 + 6

Combine like terms: 1 + 6 = 7
7 + 8x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
7 + 8x + x2 = 0

Factor a trinomial.
(7 + x)(1 + x) = 0

Subproblem 1
Set the factor '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Subproblem 2
Set the factor '(1 + x)' equal to zero and attempt to solve:

Simplifying
1 + x = 0

Solving
1 + x = 0

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

Add '-1' to each side of the equation.
1 + -1 + x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {-7, -1}