(2x+4)(x+1)-(x+1)=0

Solution for (2x+4)(x+1)-(x+1)=0 equation:

Simplifying
(2x + 4)(x + 1) + -1(x + 1) = 0

Reorder the terms:
(4 + 2x)(x + 1) + -1(x + 1) = 0

Reorder the terms:
(4 + 2x)(1 + x) + -1(x + 1) = 0

Multiply (4 + 2x) * (1 + x)
(4(1 + x) + 2x * (1 + x)) + -1(x + 1) = 0
((1 * 4 + x * 4) + 2x * (1 + x)) + -1(x + 1) = 0
((4 + 4x) + 2x * (1 + x)) + -1(x + 1) = 0
(4 + 4x + (1 * 2x + x * 2x)) + -1(x + 1) = 0
(4 + 4x + (2x + 2x2)) + -1(x + 1) = 0

Combine like terms: 4x + 2x = 6x
(4 + 6x + 2x2) + -1(x + 1) = 0

Reorder the terms:
4 + 6x + 2x2 + -1(1 + x) = 0
4 + 6x + 2x2 + (1 * -1 + x * -1) = 0
4 + 6x + 2x2 + (-1 + -1x) = 0

Reorder the terms:
4 + -1 + 6x + -1x + 2x2 = 0

Combine like terms: 4 + -1 = 3
3 + 6x + -1x + 2x2 = 0

Combine like terms: 6x + -1x = 5x
3 + 5x + 2x2 = 0

Solving
3 + 5x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + 2x)(1 + x) = 0

Subproblem 1
Set the factor '(3 + 2x)' equal to zero and attempt to solve:

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

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

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

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
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 = {-1.5, -1}