f(x)=-3(x+5)(x+2)(x-1)(x-4)

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Solution for f(x)=-3(x+5)(x+2)(x-1)(x-4) equation: 


Simplifying
f(x) = -3(x + 5)(x + 2)(x + -1)(x + -4)

Multiply f * x
fx = -3(x + 5)(x + 2)(x + -1)(x + -4)

Reorder the terms:
fx = -3(5 + x)(x + 2)(x + -1)(x + -4)

Reorder the terms:
fx = -3(5 + x)(2 + x)(x + -1)(x + -4)

Reorder the terms:
fx = -3(5 + x)(2 + x)(-1 + x)(x + -4)

Reorder the terms:
fx = -3(5 + x)(2 + x)(-1 + x)(-4 + x)

Multiply (5 + x) * (2 + x)
fx = -3(5(2 + x) + x(2 + x))(-1 + x)(-4 + x)
fx = -3((2 * 5 + x * 5) + x(2 + x))(-1 + x)(-4 + x)
fx = -3((10 + 5x) + x(2 + x))(-1 + x)(-4 + x)
fx = -3(10 + 5x + (2 * x + x * x))(-1 + x)(-4 + x)
fx = -3(10 + 5x + (2x + x2))(-1 + x)(-4 + x)

Combine like terms: 5x + 2x = 7x
fx = -3(10 + 7x + x2)(-1 + x)(-4 + x)

Multiply (10 + 7x + x2) * (-1 + x)
fx = -3(10(-1 + x) + 7x * (-1 + x) + x2(-1 + x))(-4 + x)
fx = -3((-1 * 10 + x * 10) + 7x * (-1 + x) + x2(-1 + x))(-4 + x)
fx = -3((-10 + 10x) + 7x * (-1 + x) + x2(-1 + x))(-4 + x)
fx = -3(-10 + 10x + (-1 * 7x + x * 7x) + x2(-1 + x))(-4 + x)
fx = -3(-10 + 10x + (-7x + 7x2) + x2(-1 + x))(-4 + x)
fx = -3(-10 + 10x + -7x + 7x2 + (-1 * x2 + x * x2))(-4 + x)
fx = -3(-10 + 10x + -7x + 7x2 + (-1x2 + x3))(-4 + x)

Combine like terms: 10x + -7x = 3x
fx = -3(-10 + 3x + 7x2 + -1x2 + x3)(-4 + x)

Combine like terms: 7x2 + -1x2 = 6x2
fx = -3(-10 + 3x + 6x2 + x3)(-4 + x)

Multiply (-10 + 3x + 6x2 + x3) * (-4 + x)
fx = -3(-10(-4 + x) + 3x * (-4 + x) + 6x2 * (-4 + x) + x3(-4 + x))
fx = -3((-4 * -10 + x * -10) + 3x * (-4 + x) + 6x2 * (-4 + x) + x3(-4 + x))
fx = -3((40 + -10x) + 3x * (-4 + x) + 6x2 * (-4 + x) + x3(-4 + x))
fx = -3(40 + -10x + (-4 * 3x + x * 3x) + 6x2 * (-4 + x) + x3(-4 + x))
fx = -3(40 + -10x + (-12x + 3x2) + 6x2 * (-4 + x) + x3(-4 + x))
fx = -3(40 + -10x + -12x + 3x2 + (-4 * 6x2 + x * 6x2) + x3(-4 + x))
fx = -3(40 + -10x + -12x + 3x2 + (-24x2 + 6x3) + x3(-4 + x))
fx = -3(40 + -10x + -12x + 3x2 + -24x2 + 6x3 + (-4 * x3 + x * x3))
fx = -3(40 + -10x + -12x + 3x2 + -24x2 + 6x3 + (-4x3 + x4))

Combine like terms: -10x + -12x = -22x
fx = -3(40 + -22x + 3x2 + -24x2 + 6x3 + -4x3 + x4)

Combine like terms: 3x2 + -24x2 = -21x2
fx = -3(40 + -22x + -21x2 + 6x3 + -4x3 + x4)

Combine like terms: 6x3 + -4x3 = 2x3
fx = -3(40 + -22x + -21x2 + 2x3 + x4)
fx = (40 * -3 + -22x * -3 + -21x2 * -3 + 2x3 * -3 + x4 * -3)
fx = (-120 + 66x + 63x2 + -6x3 + -3x4)

Solving
fx = -120 + 66x + 63x2 + -6x3 + -3x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -120x-1 + 66 + 63x + -6x2 + -3x3

Simplifying
f = -120x-1 + 66 + 63x + -6x2 + -3x3

Reorder the terms:
f = 66 + -120x-1 + 63x + -6x2 + -3x3

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