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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

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

Add '3' to each side of the equation.
-3 + 3 + -5x = 2 + 3

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

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

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

Simplifying
x = -1

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