(x+1)(x+6)=-6

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


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

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

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

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

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

Solving
6 + 7x + x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 6 + 7x + x2 = -6 + 6

Combine like terms: 6 + 6 = 12
12 + 7x + x2 = -6 + 6

Combine like terms: -6 + 6 = 0
12 + 7x + x2 = 0

Factor a trinomial.
(4 + x)(3 + x) = 0


Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve:

Simplifying
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4

Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve:

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x = 0 + -3
x = 0 + -3

Combine like terms: 0 + -3 = -3
x = -3

Simplifying
x = -3
Solution
x = {-4, -3}

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