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

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


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

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

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

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

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

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

Multiply (2 + 3x + x2) * (3 + x)
(2(3 + x) + 3x * (3 + x) + x2(3 + x)) = (X + -2)(x + 1)(x + 1)
((3 * 2 + x * 2) + 3x * (3 + x) + x2(3 + x)) = (X + -2)(x + 1)(x + 1)
((6 + 2x) + 3x * (3 + x) + x2(3 + x)) = (X + -2)(x + 1)(x + 1)
(6 + 2x + (3 * 3x + x * 3x) + x2(3 + x)) = (X + -2)(x + 1)(x + 1)
(6 + 2x + (9x + 3x2) + x2(3 + x)) = (X + -2)(x + 1)(x + 1)
(6 + 2x + 9x + 3x2 + (3 * x2 + x * x2)) = (X + -2)(x + 1)(x + 1)
(6 + 2x + 9x + 3x2 + (3x2 + x3)) = (X + -2)(x + 1)(x + 1)

Combine like terms: 2x + 9x = 11x
(6 + 11x + 3x2 + 3x2 + x3) = (X + -2)(x + 1)(x + 1)

Combine like terms: 3x2 + 3x2 = 6x2
(6 + 11x + 6x2 + x3) = (X + -2)(x + 1)(x + 1)

Reorder the terms:
6 + 11x + 6x2 + x3 = (-2 + X)(x + 1)(x + 1)

Reorder the terms:
6 + 11x + 6x2 + x3 = (-2 + X)(1 + x)(x + 1)

Reorder the terms:
6 + 11x + 6x2 + x3 = (-2 + X)(1 + x)(1 + x)

Multiply (-2 + X) * (1 + x)
6 + 11x + 6x2 + x3 = (-2(1 + x) + X(1 + x))(1 + x)
6 + 11x + 6x2 + x3 = ((1 * -2 + x * -2) + X(1 + x))(1 + x)
6 + 11x + 6x2 + x3 = ((-2 + -2x) + X(1 + x))(1 + x)
6 + 11x + 6x2 + x3 = (-2 + -2x + (1 * X + x * X))(1 + x)
6 + 11x + 6x2 + x3 = (-2 + -2x + (1X + xX))(1 + x)

Reorder the terms:
6 + 11x + 6x2 + x3 = (-2 + 1X + -2x + xX)(1 + x)
6 + 11x + 6x2 + x3 = (-2 + 1X + -2x + xX)(1 + x)

Multiply (-2 + 1X + -2x + xX) * (1 + x)
6 + 11x + 6x2 + x3 = (-2(1 + x) + 1X * (1 + x) + -2x * (1 + x) + xX(1 + x))
6 + 11x + 6x2 + x3 = ((1 * -2 + x * -2) + 1X * (1 + x) + -2x * (1 + x) + xX(1 + x))
6 + 11x + 6x2 + x3 = ((-2 + -2x) + 1X * (1 + x) + -2x * (1 + x) + xX(1 + x))
6 + 11x + 6x2 + x3 = (-2 + -2x + (1 * 1X + x * 1X) + -2x * (1 + x) + xX(1 + x))
6 + 11x + 6x2 + x3 = (-2 + -2x + (1X + 1xX) + -2x * (1 + x) + xX(1 + x))
6 + 11x + 6x2 + x3 = (-2 + -2x + 1X + 1xX + (1 * -2x + x * -2x) + xX(1 + x))
6 + 11x + 6x2 + x3 = (-2 + -2x + 1X + 1xX + (-2x + -2x2) + xX(1 + x))
6 + 11x + 6x2 + x3 = (-2 + -2x + 1X + 1xX + -2x + -2x2 + (1 * xX + x * xX))
6 + 11x + 6x2 + x3 = (-2 + -2x + 1X + 1xX + -2x + -2x2 + (1xX + x2X))

Reorder the terms:
6 + 11x + 6x2 + x3 = (-2 + 1X + -2x + -2x + 1xX + 1xX + -2x2 + x2X)

Combine like terms: -2x + -2x = -4x
6 + 11x + 6x2 + x3 = (-2 + 1X + -4x + 1xX + 1xX + -2x2 + x2X)

Combine like terms: 1xX + 1xX = 2xX
6 + 11x + 6x2 + x3 = (-2 + 1X + -4x + 2xX + -2x2 + x2X)

Solving
6 + 11x + 6x2 + x3 = -2 + 1X + -4x + 2xX + -2x2 + x2X

Solving for variable 'x'.

Reorder the terms:
6 + 2 + -1X + 11x + 4x + -2xX + 6x2 + 2x2 + -1x2X + x3 = -2 + 1X + -4x + 2xX + -2x2 + x2X + 2 + -1X + 4x + -2xX + 2x2 + -1x2X

Combine like terms: 6 + 2 = 8
8 + -1X + 11x + 4x + -2xX + 6x2 + 2x2 + -1x2X + x3 = -2 + 1X + -4x + 2xX + -2x2 + x2X + 2 + -1X + 4x + -2xX + 2x2 + -1x2X

Combine like terms: 11x + 4x = 15x
8 + -1X + 15x + -2xX + 6x2 + 2x2 + -1x2X + x3 = -2 + 1X + -4x + 2xX + -2x2 + x2X + 2 + -1X + 4x + -2xX + 2x2 + -1x2X

Combine like terms: 6x2 + 2x2 = 8x2
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = -2 + 1X + -4x + 2xX + -2x2 + x2X + 2 + -1X + 4x + -2xX + 2x2 + -1x2X

Reorder the terms:
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = -2 + 2 + 1X + -1X + -4x + 4x + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X

Combine like terms: -2 + 2 = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0 + 1X + -1X + -4x + 4x + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 1X + -1X + -4x + 4x + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X

Combine like terms: 1X + -1X = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0 + -4x + 4x + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = -4x + 4x + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X

Combine like terms: -4x + 4x = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0 + 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 2xX + -2xX + -2x2 + 2x2 + x2X + -1x2X

Combine like terms: 2xX + -2xX = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0 + -2x2 + 2x2 + x2X + -1x2X
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = -2x2 + 2x2 + x2X + -1x2X

Combine like terms: -2x2 + 2x2 = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0 + x2X + -1x2X
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = x2X + -1x2X

Combine like terms: x2X + -1x2X = 0
8 + -1X + 15x + -2xX + 8x2 + -1x2X + x3 = 0

The solution to this equation could not be determined.

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