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

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

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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
2 + 3x + x2 + -1x2 = -3 + 2x + x2 + -1x2

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

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

Solving
2 + 3x = -3 + 2x

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-2x' to each side of the equation.
2 + 3x + -2x = -3 + 2x + -2x

Combine like terms: 3x + -2x = 1x
2 + 1x = -3 + 2x + -2x

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

Add '-2' to each side of the equation.
2 + -2 + 1x = -3 + -2

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

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

Divide each side by '1'.
x = -5

Simplifying
x = -5