2x(x+1)+x+1=0

Solution for 2x(x+1)+x+1=0 equation:

Simplifying
2x(x + 1) + x + 1 = 0

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

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

Combine like terms: 2x + x = 3x
1 + 3x + 2x2 = 0

Solving
1 + 3x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + x)(1 + 2x) = 0

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

Simplifying
1 + 2x = 0

Solving
1 + 2x = 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 + 2x = 0 + -1

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

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

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-1, -0.5}