p(x)=(x+5)(x-10)(x+8)

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Solution for p(x)=(x+5)(x-10)(x+8) equation: 


Simplifying
p(x) = (x + 5)(x + -10)(x + 8)

Multiply p * x
px = (x + 5)(x + -10)(x + 8)

Reorder the terms:
px = (5 + x)(x + -10)(x + 8)

Reorder the terms:
px = (5 + x)(-10 + x)(x + 8)

Reorder the terms:
px = (5 + x)(-10 + x)(8 + x)

Multiply (5 + x) * (-10 + x)
px = (5(-10 + x) + x(-10 + x))(8 + x)
px = ((-10 * 5 + x * 5) + x(-10 + x))(8 + x)
px = ((-50 + 5x) + x(-10 + x))(8 + x)
px = (-50 + 5x + (-10 * x + x * x))(8 + x)
px = (-50 + 5x + (-10x + x2))(8 + x)

Combine like terms: 5x + -10x = -5x
px = (-50 + -5x + x2)(8 + x)

Multiply (-50 + -5x + x2) * (8 + x)
px = (-50(8 + x) + -5x * (8 + x) + x2(8 + x))
px = ((8 * -50 + x * -50) + -5x * (8 + x) + x2(8 + x))
px = ((-400 + -50x) + -5x * (8 + x) + x2(8 + x))
px = (-400 + -50x + (8 * -5x + x * -5x) + x2(8 + x))
px = (-400 + -50x + (-40x + -5x2) + x2(8 + x))
px = (-400 + -50x + -40x + -5x2 + (8 * x2 + x * x2))
px = (-400 + -50x + -40x + -5x2 + (8x2 + x3))

Combine like terms: -50x + -40x = -90x
px = (-400 + -90x + -5x2 + 8x2 + x3)

Combine like terms: -5x2 + 8x2 = 3x2
px = (-400 + -90x + 3x2 + x3)

Solving
px = -400 + -90x + 3x2 + x3

Solving for variable 'p'.

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

Divide each side by 'x'.
p = -400x-1 + -90 + 3x + x2

Simplifying
p = -400x-1 + -90 + 3x + x2

Reorder the terms:
p = -90 + -400x-1 + 3x + x2

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