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

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

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

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

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

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

Combine like terms: 1x + 1x = 2x
(1 + 2x + x2) + (x + 1) + -6 = 0

Reorder the terms:
1 + 2x + x2 + (1 + x) + -6 = 0

Remove parenthesis around (1 + x)
1 + 2x + x2 + 1 + x + -6 = 0

Reorder the terms:
1 + 1 + -6 + 2x + x + x2 = 0

Combine like terms: 1 + 1 = 2
2 + -6 + 2x + x + x2 = 0

Combine like terms: 2 + -6 = -4
-4 + 2x + x + x2 = 0

Combine like terms: 2x + x = 3x
-4 + 3x + x2 = 0

Solving
-4 + 3x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
-4 + -1x = 0

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

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4
Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 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 + -1x = 0 + -1

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

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

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Solution
x = {-4, 1}