(x+6)(x+1)=0

Solution for (x+6)(x+1)=0 equation:

Simplifying
(x + 6)(x + 1) = 0

Reorder the terms:
(6 + x)(x + 1) = 0

Reorder the terms:
(6 + x)(1 + x) = 0

Multiply (6 + x) * (1 + x)
(6(1 + x) + x(1 + x)) = 0
((1 * 6 + x * 6) + x(1 + x)) = 0
((6 + 6x) + x(1 + x)) = 0
(6 + 6x + (1 * x + x * x)) = 0
(6 + 6x + (1x + x2)) = 0

Combine like terms: 6x + 1x = 7x
(6 + 7x + x2) = 0

Solving
6 + 7x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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 = {-6, -1}