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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
-2 + -1x = -1 + 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 + -1x + -2x = -1 + 2x + -2x

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

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

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

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

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

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333

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