x^3-PX^2+qx-r=0

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Solution for x^3-PX^2+qx-r=0 equation:


Simplifying
x3 + -1PX2 + qx + -1r = 0

Reorder the terms:
-1PX2 + qx + -1r + x3 = 0

Solving
-1PX2 + qx + -1r + x3 = 0

Solving for variable 'P'.

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

Add '-1qx' to each side of the equation.
-1PX2 + qx + -1r + -1qx + x3 = 0 + -1qx

Reorder the terms:
-1PX2 + qx + -1qx + -1r + x3 = 0 + -1qx

Combine like terms: qx + -1qx = 0
-1PX2 + 0 + -1r + x3 = 0 + -1qx
-1PX2 + -1r + x3 = 0 + -1qx
Remove the zero:
-1PX2 + -1r + x3 = -1qx

Add 'r' to each side of the equation.
-1PX2 + -1r + r + x3 = -1qx + r

Combine like terms: -1r + r = 0
-1PX2 + 0 + x3 = -1qx + r
-1PX2 + x3 = -1qx + r

Add '-1x3' to each side of the equation.
-1PX2 + x3 + -1x3 = -1qx + r + -1x3

Combine like terms: x3 + -1x3 = 0
-1PX2 + 0 = -1qx + r + -1x3
-1PX2 = -1qx + r + -1x3

Divide each side by '-1X2'.
P = qxX-2 + -1rX-2 + x3X-2

Simplifying
P = qxX-2 + -1rX-2 + x3X-2

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