X(x-2)(x-a)=x(x^2-4)-3x(x-2)

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Solution for X(x-2)(x-a)=x(x^2-4)-3x(x-2) equation:


Simplifying
X(x + -2)(x + -1a) = x(x2 + -4) + -3x(x + -2)

Reorder the terms:
X(-2 + x)(x + -1a) = x(x2 + -4) + -3x(x + -2)

Reorder the terms:
X(-2 + x)(-1a + x) = x(x2 + -4) + -3x(x + -2)

Multiply (-2 + x) * (-1a + x)
X(-2(-1a + x) + x(-1a + x)) = x(x2 + -4) + -3x(x + -2)
X((-1a * -2 + x * -2) + x(-1a + x)) = x(x2 + -4) + -3x(x + -2)
X((2a + -2x) + x(-1a + x)) = x(x2 + -4) + -3x(x + -2)
X(2a + -2x + (-1a * x + x * x)) = x(x2 + -4) + -3x(x + -2)
X(2a + -2x + (-1ax + x2)) = x(x2 + -4) + -3x(x + -2)

Reorder the terms:
X(2a + -1ax + -2x + x2) = x(x2 + -4) + -3x(x + -2)
X(2a + -1ax + -2x + x2) = x(x2 + -4) + -3x(x + -2)
(2a * X + -1ax * X + -2x * X + x2 * X) = x(x2 + -4) + -3x(x + -2)
(2aX + -1axX + -2xX + x2X) = x(x2 + -4) + -3x(x + -2)

Reorder the terms:
2aX + -1axX + -2xX + x2X = x(-4 + x2) + -3x(x + -2)
2aX + -1axX + -2xX + x2X = (-4 * x + x2 * x) + -3x(x + -2)
2aX + -1axX + -2xX + x2X = (-4x + x3) + -3x(x + -2)

Reorder the terms:
2aX + -1axX + -2xX + x2X = -4x + x3 + -3x(-2 + x)
2aX + -1axX + -2xX + x2X = -4x + x3 + (-2 * -3x + x * -3x)
2aX + -1axX + -2xX + x2X = -4x + x3 + (6x + -3x2)

Reorder the terms:
2aX + -1axX + -2xX + x2X = -4x + 6x + -3x2 + x3

Combine like terms: -4x + 6x = 2x
2aX + -1axX + -2xX + x2X = 2x + -3x2 + x3

Solving
2aX + -1axX + -2xX + x2X = 2x + -3x2 + x3

Solving for variable 'a'.

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

Add '2xX' to each side of the equation.
2aX + -1axX + -2xX + 2xX + x2X = 2x + -3x2 + 2xX + x3

Combine like terms: -2xX + 2xX = 0
2aX + -1axX + 0 + x2X = 2x + -3x2 + 2xX + x3
2aX + -1axX + x2X = 2x + -3x2 + 2xX + x3

Reorder the terms:
2aX + -1axX + x2X = 2x + 2xX + -3x2 + x3

Add '-1x2X' to each side of the equation.
2aX + -1axX + x2X + -1x2X = 2x + 2xX + -3x2 + -1x2X + x3

Combine like terms: x2X + -1x2X = 0
2aX + -1axX + 0 = 2x + 2xX + -3x2 + -1x2X + x3
2aX + -1axX = 2x + 2xX + -3x2 + -1x2X + x3

Reorder the terms:
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 2x + -2x + 2xX + -2xX + -3x2 + 3x2 + -1x2X + x2X + x3 + -1x3

Combine like terms: 2x + -2x = 0
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 0 + 2xX + -2xX + -3x2 + 3x2 + -1x2X + x2X + x3 + -1x3
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 2xX + -2xX + -3x2 + 3x2 + -1x2X + x2X + x3 + -1x3

Combine like terms: 2xX + -2xX = 0
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 0 + -3x2 + 3x2 + -1x2X + x2X + x3 + -1x3
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = -3x2 + 3x2 + -1x2X + x2X + x3 + -1x3

Combine like terms: -3x2 + 3x2 = 0
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 0 + -1x2X + x2X + x3 + -1x3
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = -1x2X + x2X + x3 + -1x3

Combine like terms: -1x2X + x2X = 0
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 0 + x3 + -1x3
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2aX + -1axX + -2x + -2xX + 3x2 + x2X + -1x3 = 0

The solution to this equation could not be determined.

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