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

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


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

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

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

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

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

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

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

Combine like terms: 1x + 1x = 2x
fx = -2(1 + 2x + x2)(1 + x)(-5 + x)

Multiply (1 + 2x + x2) * (1 + x)
fx = -2(1(1 + x) + 2x * (1 + x) + x2(1 + x))(-5 + x)
fx = -2((1 * 1 + x * 1) + 2x * (1 + x) + x2(1 + x))(-5 + x)
fx = -2((1 + 1x) + 2x * (1 + x) + x2(1 + x))(-5 + x)
fx = -2(1 + 1x + (1 * 2x + x * 2x) + x2(1 + x))(-5 + x)
fx = -2(1 + 1x + (2x + 2x2) + x2(1 + x))(-5 + x)
fx = -2(1 + 1x + 2x + 2x2 + (1 * x2 + x * x2))(-5 + x)
fx = -2(1 + 1x + 2x + 2x2 + (1x2 + x3))(-5 + x)

Combine like terms: 1x + 2x = 3x
fx = -2(1 + 3x + 2x2 + 1x2 + x3)(-5 + x)

Combine like terms: 2x2 + 1x2 = 3x2
fx = -2(1 + 3x + 3x2 + x3)(-5 + x)

Multiply (1 + 3x + 3x2 + x3) * (-5 + x)
fx = -2(1(-5 + x) + 3x * (-5 + x) + 3x2 * (-5 + x) + x3(-5 + x))
fx = -2((-5 * 1 + x * 1) + 3x * (-5 + x) + 3x2 * (-5 + x) + x3(-5 + x))
fx = -2((-5 + 1x) + 3x * (-5 + x) + 3x2 * (-5 + x) + x3(-5 + x))
fx = -2(-5 + 1x + (-5 * 3x + x * 3x) + 3x2 * (-5 + x) + x3(-5 + x))
fx = -2(-5 + 1x + (-15x + 3x2) + 3x2 * (-5 + x) + x3(-5 + x))
fx = -2(-5 + 1x + -15x + 3x2 + (-5 * 3x2 + x * 3x2) + x3(-5 + x))
fx = -2(-5 + 1x + -15x + 3x2 + (-15x2 + 3x3) + x3(-5 + x))
fx = -2(-5 + 1x + -15x + 3x2 + -15x2 + 3x3 + (-5 * x3 + x * x3))
fx = -2(-5 + 1x + -15x + 3x2 + -15x2 + 3x3 + (-5x3 + x4))

Combine like terms: 1x + -15x = -14x
fx = -2(-5 + -14x + 3x2 + -15x2 + 3x3 + -5x3 + x4)

Combine like terms: 3x2 + -15x2 = -12x2
fx = -2(-5 + -14x + -12x2 + 3x3 + -5x3 + x4)

Combine like terms: 3x3 + -5x3 = -2x3
fx = -2(-5 + -14x + -12x2 + -2x3 + x4)
fx = (-5 * -2 + -14x * -2 + -12x2 * -2 + -2x3 * -2 + x4 * -2)
fx = (10 + 28x + 24x2 + 4x3 + -2x4)

Solving
fx = 10 + 28x + 24x2 + 4x3 + -2x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 10x-1 + 28 + 24x + 4x2 + -2x3

Simplifying
f = 10x-1 + 28 + 24x + 4x2 + -2x3

Reorder the terms:
f = 28 + 10x-1 + 24x + 4x2 + -2x3

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