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

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

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

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

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

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

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

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

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

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

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

Solving
2 + 3x = 1x

Solving for variable 'x'.

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

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

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

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

Add '-2' to each side of the equation.
2 + -2 + 2x = 0 + -2

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

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

Divide each side by '2'.
x = -1

Simplifying
x = -1