F(x)=x(x-p)(x-q)*2

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Solution for F(x)=x(x-p)(x-q)*2 equation: 


Simplifying
F(x) = x(x + -1p)(x + -1q) * 2

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

Reorder the terms:
xF = x(-1p + x)(x + -1q) * 2

Reorder the terms:
xF = x(-1p + x)(-1q + x) * 2

Reorder the terms for easier multiplication:
xF = 2x(-1p + x)(-1q + x)

Multiply (-1p + x) * (-1q + x)
xF = 2x(-1p * (-1q + x) + x(-1q + x))
xF = 2x((-1q * -1p + x * -1p) + x(-1q + x))
xF = 2x((1pq + -1px) + x(-1q + x))
xF = 2x(1pq + -1px + (-1q * x + x * x))
xF = 2x(1pq + -1px + (-1qx + x2))
xF = 2x(1pq + -1px + -1qx + x2)
xF = (1pq * 2x + -1px * 2x + -1qx * 2x + x2 * 2x)
xF = (2pqx + -2px2 + -2qx2 + 2x3)

Solving
xF = 2pqx + -2px2 + -2qx2 + 2x3

Solving for variable 'x'.

Reorder the terms:
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 2pqx + -2px2 + -2qx2 + 2x3 + -2pqx + 2px2 + 2qx2 + -2x3

Reorder the terms:
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 2pqx + -2pqx + -2px2 + 2px2 + -2qx2 + 2qx2 + 2x3 + -2x3

Combine like terms: 2pqx + -2pqx = 0
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 0 + -2px2 + 2px2 + -2qx2 + 2qx2 + 2x3 + -2x3
-2pqx + 2px2 + 2qx2 + xF + -2x3 = -2px2 + 2px2 + -2qx2 + 2qx2 + 2x3 + -2x3

Combine like terms: -2px2 + 2px2 = 0
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 0 + -2qx2 + 2qx2 + 2x3 + -2x3
-2pqx + 2px2 + 2qx2 + xF + -2x3 = -2qx2 + 2qx2 + 2x3 + -2x3

Combine like terms: -2qx2 + 2qx2 = 0
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 0 + 2x3 + -2x3
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 2x3 + -2x3

Combine like terms: 2x3 + -2x3 = 0
-2pqx + 2px2 + 2qx2 + xF + -2x3 = 0

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

Simplifying
-2pq + 2px + 2qx + F + -2x2 = 0

Reorder the terms:
F + -2pq + 2px + 2qx + -2x2 = 0

Solving
F + -2pq + 2px + 2qx + -2x2 = 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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