p(x)=x(x-5)(x-2)(x+3)

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Solution for p(x)=x(x-5)(x-2)(x+3) equation: 


Simplifying
p(x) = x(x + -5)(x + -2)(x + 3)

Multiply p * x
px = x(x + -5)(x + -2)(x + 3)

Reorder the terms:
px = x(-5 + x)(x + -2)(x + 3)

Reorder the terms:
px = x(-5 + x)(-2 + x)(x + 3)

Reorder the terms:
px = x(-5 + x)(-2 + x)(3 + x)

Multiply (-5 + x) * (-2 + x)
px = x(-5(-2 + x) + x(-2 + x))(3 + x)
px = x((-2 * -5 + x * -5) + x(-2 + x))(3 + x)
px = x((10 + -5x) + x(-2 + x))(3 + x)
px = x(10 + -5x + (-2 * x + x * x))(3 + x)
px = x(10 + -5x + (-2x + x2))(3 + x)

Combine like terms: -5x + -2x = -7x
px = x(10 + -7x + x2)(3 + x)

Multiply (10 + -7x + x2) * (3 + x)
px = x(10(3 + x) + -7x * (3 + x) + x2(3 + x))
px = x((3 * 10 + x * 10) + -7x * (3 + x) + x2(3 + x))
px = x((30 + 10x) + -7x * (3 + x) + x2(3 + x))
px = x(30 + 10x + (3 * -7x + x * -7x) + x2(3 + x))
px = x(30 + 10x + (-21x + -7x2) + x2(3 + x))
px = x(30 + 10x + -21x + -7x2 + (3 * x2 + x * x2))
px = x(30 + 10x + -21x + -7x2 + (3x2 + x3))

Combine like terms: 10x + -21x = -11x
px = x(30 + -11x + -7x2 + 3x2 + x3)

Combine like terms: -7x2 + 3x2 = -4x2
px = x(30 + -11x + -4x2 + x3)
px = (30 * x + -11x * x + -4x2 * x + x3 * x)
px = (30x + -11x2 + -4x3 + x4)

Solving
px = 30x + -11x2 + -4x3 + x4

Solving for variable 'p'.

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

Divide each side by 'x'.
p = 30 + -11x + -4x2 + x3

Simplifying
p = 30 + -11x + -4x2 + x3

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