x^3-x^2-px+q=0

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Solution for x^3-x^2-px+q=0 equation:


Simplifying
x3 + -1x2 + -1px + q = 0

Reorder the terms:
-1px + q + -1x2 + x3 = 0

Solving
-1px + q + -1x2 + x3 = 0

Solving for variable 'p'.

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

Add '-1q' to each side of the equation.
-1px + q + -1x2 + -1q + x3 = 0 + -1q

Reorder the terms:
-1px + q + -1q + -1x2 + x3 = 0 + -1q

Combine like terms: q + -1q = 0
-1px + 0 + -1x2 + x3 = 0 + -1q
-1px + -1x2 + x3 = 0 + -1q
Remove the zero:
-1px + -1x2 + x3 = -1q

Add 'x2' to each side of the equation.
-1px + -1x2 + x2 + x3 = -1q + x2

Combine like terms: -1x2 + x2 = 0
-1px + 0 + x3 = -1q + x2
-1px + x3 = -1q + x2

Add '-1x3' to each side of the equation.
-1px + x3 + -1x3 = -1q + x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-1px + 0 = -1q + x2 + -1x3
-1px = -1q + x2 + -1x3

Divide each side by '-1x'.
p = qx-1 + -1x + x2

Simplifying
p = qx-1 + -1x + x2

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