F(x)=x^3+px^2+qx

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Solution for F(x)=x^3+px^2+qx equation: 


Simplifying
F(x) = x3 + px2 + qx

Multiply F * x
xF = x3 + px2 + qx

Reorder the terms:
xF = px2 + qx + x3

Solving
xF = px2 + qx + x3

Solving for variable 'x'.

Reorder the terms:
-1px2 + -1qx + xF + -1x3 = px2 + qx + x3 + -1px2 + -1qx + -1x3

Reorder the terms:
-1px2 + -1qx + xF + -1x3 = px2 + -1px2 + qx + -1qx + x3 + -1x3

Combine like terms: px2 + -1px2 = 0
-1px2 + -1qx + xF + -1x3 = 0 + qx + -1qx + x3 + -1x3
-1px2 + -1qx + xF + -1x3 = qx + -1qx + x3 + -1x3

Combine like terms: qx + -1qx = 0
-1px2 + -1qx + xF + -1x3 = 0 + x3 + -1x3
-1px2 + -1qx + xF + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
-1px2 + -1qx + xF + -1x3 = 0

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

Simplifying
-1px + -1q + F + -1x2 = 0

Reorder the terms:
F + -1px + -1q + -1x2 = 0

Solving
F + -1px + -1q + -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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