(x+1)(x-1)-(3x+4)(x+1)=2(x+2)-x-3

Solution for (x+1)(x-1)-(3x+4)(x+1)=2(x+2)-x-3 equation:

Simplifying
(x + 1)(x + -1) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3

Reorder the terms:
(1 + x)(x + -1) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3

Reorder the terms:
(1 + x)(-1 + x) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3

Multiply (1 + x) * (-1 + x)
(1(-1 + x) + x(-1 + x)) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3
((-1 * 1 + x * 1) + x(-1 + x)) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3
((-1 + 1x) + x(-1 + x)) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3
(-1 + 1x + (-1 * x + x * x)) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3
(-1 + 1x + (-1x + x2)) + -1(3x + 4)(x + 1) = 2(x + 2) + -1x + -3

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

Reorder the terms:
-1 + x2 + -1(4 + 3x)(x + 1) = 2(x + 2) + -1x + -3

Reorder the terms:
-1 + x2 + -1(4 + 3x)(1 + x) = 2(x + 2) + -1x + -3

Multiply (4 + 3x) * (1 + x)
-1 + x2 + -1(4(1 + x) + 3x * (1 + x)) = 2(x + 2) + -1x + -3
-1 + x2 + -1((1 * 4 + x * 4) + 3x * (1 + x)) = 2(x + 2) + -1x + -3
-1 + x2 + -1((4 + 4x) + 3x * (1 + x)) = 2(x + 2) + -1x + -3
-1 + x2 + -1(4 + 4x + (1 * 3x + x * 3x)) = 2(x + 2) + -1x + -3
-1 + x2 + -1(4 + 4x + (3x + 3x2)) = 2(x + 2) + -1x + -3

Combine like terms: 4x + 3x = 7x
-1 + x2 + -1(4 + 7x + 3x2) = 2(x + 2) + -1x + -3
-1 + x2 + (4 * -1 + 7x * -1 + 3x2 * -1) = 2(x + 2) + -1x + -3
-1 + x2 + (-4 + -7x + -3x2) = 2(x + 2) + -1x + -3

Reorder the terms:
-1 + -4 + -7x + x2 + -3x2 = 2(x + 2) + -1x + -3

Combine like terms: -1 + -4 = -5
-5 + -7x + x2 + -3x2 = 2(x + 2) + -1x + -3

Combine like terms: x2 + -3x2 = -2x2
-5 + -7x + -2x2 = 2(x + 2) + -1x + -3

Reorder the terms:
-5 + -7x + -2x2 = 2(2 + x) + -1x + -3
-5 + -7x + -2x2 = (2 * 2 + x * 2) + -1x + -3
-5 + -7x + -2x2 = (4 + 2x) + -1x + -3

Reorder the terms:
-5 + -7x + -2x2 = 4 + -3 + 2x + -1x

Combine like terms: 4 + -3 = 1
-5 + -7x + -2x2 = 1 + 2x + -1x

Combine like terms: 2x + -1x = 1x
-5 + -7x + -2x2 = 1 + 1x

Solving
-5 + -7x + -2x2 = 1 + 1x

Solving for variable 'x'.

Reorder the terms:
-5 + -1 + -7x + -1x + -2x2 = 1 + 1x + -1 + -1x

Combine like terms: -5 + -1 = -6
-6 + -7x + -1x + -2x2 = 1 + 1x + -1 + -1x

Combine like terms: -7x + -1x = -8x
-6 + -8x + -2x2 = 1 + 1x + -1 + -1x

Reorder the terms:
-6 + -8x + -2x2 = 1 + -1 + 1x + -1x

Combine like terms: 1 + -1 = 0
-6 + -8x + -2x2 = 0 + 1x + -1x
-6 + -8x + -2x2 = 1x + -1x

Combine like terms: 1x + -1x = 0
-6 + -8x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 4x + x2) = 0

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

Ignore the factor -2.
Subproblem 1
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
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 = {-3, -1}