(x+1)-(5+x)*(x+1)=

Solution for (x+1)-(5+x)*(x+1)= equation:

Simplifying
(x + 1) + -1(5 + x)(x + 1) = 0

Reorder the terms:
(1 + x) + -1(5 + x)(x + 1) = 0

Remove parenthesis around (1 + x)
1 + x + -1(5 + x)(x + 1) = 0

Reorder the terms:
1 + x + -1(5 + x)(1 + x) = 0

Multiply (5 + x) * (1 + x)
1 + x + -1(5(1 + x) + x(1 + x)) = 0
1 + x + -1((1 * 5 + x * 5) + x(1 + x)) = 0
1 + x + -1((5 + 5x) + x(1 + x)) = 0
1 + x + -1(5 + 5x + (1 * x + x * x)) = 0
1 + x + -1(5 + 5x + (1x + x2)) = 0

Combine like terms: 5x + 1x = 6x
1 + x + -1(5 + 6x + x2) = 0
1 + x + (5 * -1 + 6x * -1 + x2 * -1) = 0
1 + x + (-5 + -6x + -1x2) = 0

Reorder the terms:
1 + -5 + x + -6x + -1x2 = 0

Combine like terms: 1 + -5 = -4
-4 + x + -6x + -1x2 = 0

Combine like terms: x + -6x = -5x
-4 + -5x + -1x2 = 0

Solving
-4 + -5x + -1x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(4 + 5x + x2) = 0

Factor a trinomial.
-1((4 + x)(1 + x)) = 0

Ignore the factor -1.
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 '(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 = {-4, -1}