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

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


Simplifying
(x + -3)(x2 + -1px + q) = 0

Reorder the terms:
(-3 + x)(x2 + -1px + q) = 0

Reorder the terms:
(-3 + x)(-1px + q + x2) = 0

Multiply (-3 + x) * (-1px + q + x2)
(-3(-1px + q + x2) + x(-1px + q + x2)) = 0
((-1px * -3 + q * -3 + x2 * -3) + x(-1px + q + x2)) = 0
((3px + -3q + -3x2) + x(-1px + q + x2)) = 0
(3px + -3q + -3x2 + (-1px * x + q * x + x2 * x)) = 0
(3px + -3q + -3x2 + (-1px2 + qx + x3)) = 0

Reorder the terms:
(3px + -1px2 + -3q + qx + -3x2 + x3) = 0
(3px + -1px2 + -3q + qx + -3x2 + x3) = 0

Solving
3px + -1px2 + -3q + qx + -3x2 + x3 = 0

Solving for variable 'p'.

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

Add '3q' to each side of the equation.
3px + -1px2 + -3q + qx + -3x2 + 3q + x3 = 0 + 3q

Reorder the terms:
3px + -1px2 + -3q + 3q + qx + -3x2 + x3 = 0 + 3q

Combine like terms: -3q + 3q = 0
3px + -1px2 + 0 + qx + -3x2 + x3 = 0 + 3q
3px + -1px2 + qx + -3x2 + x3 = 0 + 3q
Remove the zero:
3px + -1px2 + qx + -3x2 + x3 = 3q

Add '-1qx' to each side of the equation.
3px + -1px2 + qx + -3x2 + -1qx + x3 = 3q + -1qx

Reorder the terms:
3px + -1px2 + qx + -1qx + -3x2 + x3 = 3q + -1qx

Combine like terms: qx + -1qx = 0
3px + -1px2 + 0 + -3x2 + x3 = 3q + -1qx
3px + -1px2 + -3x2 + x3 = 3q + -1qx

Add '3x2' to each side of the equation.
3px + -1px2 + -3x2 + 3x2 + x3 = 3q + -1qx + 3x2

Combine like terms: -3x2 + 3x2 = 0
3px + -1px2 + 0 + x3 = 3q + -1qx + 3x2
3px + -1px2 + x3 = 3q + -1qx + 3x2

Add '-1x3' to each side of the equation.
3px + -1px2 + x3 + -1x3 = 3q + -1qx + 3x2 + -1x3

Combine like terms: x3 + -1x3 = 0
3px + -1px2 + 0 = 3q + -1qx + 3x2 + -1x3
3px + -1px2 = 3q + -1qx + 3x2 + -1x3

Reorder the terms:
3px + -1px2 + -3q + qx + -3x2 + x3 = 3q + -3q + -1qx + qx + 3x2 + -3x2 + -1x3 + x3

Combine like terms: 3q + -3q = 0
3px + -1px2 + -3q + qx + -3x2 + x3 = 0 + -1qx + qx + 3x2 + -3x2 + -1x3 + x3
3px + -1px2 + -3q + qx + -3x2 + x3 = -1qx + qx + 3x2 + -3x2 + -1x3 + x3

Combine like terms: -1qx + qx = 0
3px + -1px2 + -3q + qx + -3x2 + x3 = 0 + 3x2 + -3x2 + -1x3 + x3
3px + -1px2 + -3q + qx + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3

Combine like terms: 3x2 + -3x2 = 0
3px + -1px2 + -3q + qx + -3x2 + x3 = 0 + -1x3 + x3
3px + -1px2 + -3q + qx + -3x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
3px + -1px2 + -3q + qx + -3x2 + x3 = 0

The solution to this equation could not be determined.

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