F(x)=x(x-2)(x-a)

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Solution for F(x)=x(x-2)(x-a) equation: 


Simplifying
F(x) = x(x + -2)(x + -1a)

Multiply F * x
xF = x(x + -2)(x + -1a)

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

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

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

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

Solving
xF = 2ax + -1ax2 + -2x2 + x3

Solving for variable 'x'.

Reorder the terms:
-2ax + ax2 + xF + 2x2 + -1x3 = 2ax + -1ax2 + -2x2 + x3 + -2ax + ax2 + 2x2 + -1x3

Reorder the terms:
-2ax + ax2 + xF + 2x2 + -1x3 = 2ax + -2ax + -1ax2 + ax2 + -2x2 + 2x2 + x3 + -1x3

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

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

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

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-2a + ax + F + 2x + -1x2) = 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 + F + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
-2a + ax + F + 2x + -1x2 = 0

Reorder the terms:
F + -2a + ax + 2x + -1x2 = 0

Solving
F + -2a + ax + 2x + -1x2 = 0

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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