f(x)=(x-3)(x^2+px+q)

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Solution for f(x)=(x-3)(x^2+px+q) equation: 


Simplifying
f(x) = (x + -3)(x2 + px + q)

Multiply f * x
fx = (x + -3)(x2 + px + q)

Reorder the terms:
fx = (-3 + x)(x2 + px + q)

Reorder the terms:
fx = (-3 + x)(px + q + x2)

Multiply (-3 + x) * (px + q + x2)
fx = (-3(px + q + x2) + x(px + q + x2))
fx = ((px * -3 + q * -3 + x2 * -3) + x(px + q + x2))
fx = ((-3px + -3q + -3x2) + x(px + q + x2))
fx = (-3px + -3q + -3x2 + (px * x + q * x + x2 * x))
fx = (-3px + -3q + -3x2 + (px2 + qx + x3))

Reorder the terms:
fx = (-3px + px2 + -3q + qx + -3x2 + x3)
fx = (-3px + px2 + -3q + qx + -3x2 + x3)

Solving
fx = -3px + px2 + -3q + qx + -3x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -3p + px + -3qx-1 + q + -3x + x2

Simplifying
f = -3p + px + -3qx-1 + q + -3x + x2

Reorder the terms:
f = -3p + px + q + -3qx-1 + -3x + x2

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