p(x)=(m-1)x^3+(2-m)x^2+mx-1

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Solution for p(x)=(m-1)x^3+(2-m)x^2+mx-1 equation: 


Simplifying
p(x) = (m + -1) * x3 + (2 + -1m) * x2 + mx + -1

Multiply p * x
px = (m + -1) * x3 + (2 + -1m) * x2 + mx + -1

Reorder the terms:
px = (-1 + m) * x3 + (2 + -1m) * x2 + mx + -1

Reorder the terms for easier multiplication:
px = x3(-1 + m) + (2 + -1m) * x2 + mx + -1
px = (-1 * x3 + m * x3) + (2 + -1m) * x2 + mx + -1

Reorder the terms:
px = (mx3 + -1x3) + (2 + -1m) * x2 + mx + -1
px = (mx3 + -1x3) + (2 + -1m) * x2 + mx + -1

Reorder the terms for easier multiplication:
px = mx3 + -1x3 + x2(2 + -1m) + mx + -1
px = mx3 + -1x3 + (2 * x2 + -1m * x2) + mx + -1

Reorder the terms:
px = mx3 + -1x3 + (-1mx2 + 2x2) + mx + -1
px = mx3 + -1x3 + (-1mx2 + 2x2) + mx + -1

Reorder the terms:
px = -1 + mx + -1mx2 + mx3 + 2x2 + -1x3

Solving
px = -1 + mx + -1mx2 + mx3 + 2x2 + -1x3

Solving for variable 'p'.

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

Divide each side by 'x'.
p = -1x-1 + m + -1mx + mx2 + 2x + -1x2

Simplifying
p = -1x-1 + m + -1mx + mx2 + 2x + -1x2

Reorder the terms:
p = m + -1mx + mx2 + -1x-1 + 2x + -1x2

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