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

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


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

Reorder the terms:
x(-4 + x2) + -3x(x + -2) = x(x + -2)(x + -1a)
(-4 * x + x2 * x) + -3x(x + -2) = x(x + -2)(x + -1a)
(-4x + x3) + -3x(x + -2) = x(x + -2)(x + -1a)

Reorder the terms:
-4x + x3 + -3x(-2 + x) = x(x + -2)(x + -1a)
-4x + x3 + (-2 * -3x + x * -3x) = x(x + -2)(x + -1a)
-4x + x3 + (6x + -3x2) = x(x + -2)(x + -1a)

Reorder the terms:
-4x + 6x + -3x2 + x3 = x(x + -2)(x + -1a)

Combine like terms: -4x + 6x = 2x
2x + -3x2 + x3 = x(x + -2)(x + -1a)

Reorder the terms:
2x + -3x2 + x3 = x(-2 + x)(x + -1a)

Reorder the terms:
2x + -3x2 + x3 = x(-2 + x)(-1a + x)

Multiply (-2 + x) * (-1a + x)
2x + -3x2 + x3 = x(-2(-1a + x) + x(-1a + x))
2x + -3x2 + x3 = x((-1a * -2 + x * -2) + x(-1a + x))
2x + -3x2 + x3 = x((2a + -2x) + x(-1a + x))
2x + -3x2 + x3 = x(2a + -2x + (-1a * x + x * x))
2x + -3x2 + x3 = x(2a + -2x + (-1ax + x2))

Reorder the terms:
2x + -3x2 + x3 = x(2a + -1ax + -2x + x2)
2x + -3x2 + x3 = x(2a + -1ax + -2x + x2)
2x + -3x2 + x3 = (2a * x + -1ax * x + -2x * x + x2 * x)
2x + -3x2 + x3 = (2ax + -1ax2 + -2x2 + x3)

Add '-1x3' to each side of the equation.
2x + -3x2 + x3 + -1x3 = 2ax + -1ax2 + -2x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + -3x2 + 0 = 2ax + -1ax2 + -2x2 + x3 + -1x3
2x + -3x2 = 2ax + -1ax2 + -2x2 + x3 + -1x3

Combine like terms: x3 + -1x3 = 0
2x + -3x2 = 2ax + -1ax2 + -2x2 + 0
2x + -3x2 = 2ax + -1ax2 + -2x2

Solving
2x + -3x2 = 2ax + -1ax2 + -2x2

Solving for variable 'x'.

Reorder the terms:
-2ax + ax2 + 2x + -3x2 + 2x2 = 2ax + -1ax2 + -2x2 + -2ax + ax2 + 2x2

Combine like terms: -3x2 + 2x2 = -1x2
-2ax + ax2 + 2x + -1x2 = 2ax + -1ax2 + -2x2 + -2ax + ax2 + 2x2

Reorder the terms:
-2ax + ax2 + 2x + -1x2 = 2ax + -2ax + -1ax2 + ax2 + -2x2 + 2x2

Combine like terms: 2ax + -2ax = 0
-2ax + ax2 + 2x + -1x2 = 0 + -1ax2 + ax2 + -2x2 + 2x2
-2ax + ax2 + 2x + -1x2 = -1ax2 + ax2 + -2x2 + 2x2

Combine like terms: -1ax2 + ax2 = 0
-2ax + ax2 + 2x + -1x2 = 0 + -2x2 + 2x2
-2ax + ax2 + 2x + -1x2 = -2x2 + 2x2

Combine like terms: -2x2 + 2x2 = 0
-2ax + ax2 + 2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2a + ax + 2 + -1x) = 0

Subproblem 1

Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0

Subproblem 2

Set the factor '(-2a + ax + 2 + -1x)' equal to zero and attempt to solve: Simplifying -2a + ax + 2 + -1x = 0 Reorder the terms: 2 + -2a + ax + -1x = 0 Solving 2 + -2a + ax + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2a + ax + -2 + -1x = 0 + -2 Reorder the terms: 2 + -2 + -2a + ax + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -2a + ax + -1x = 0 + -2 -2a + ax + -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -2a + ax + -1x = -2 Add '2a' to each side of the equation. -2a + ax + 2a + -1x = -2 + 2a Reorder the terms: -2a + 2a + ax + -1x = -2 + 2a Combine like terms: -2a + 2a = 0 0 + ax + -1x = -2 + 2a ax + -1x = -2 + 2a The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.

Solution

x = {0}

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