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

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


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

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

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

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

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

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

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

Combine like terms: 2x + 2x = 4x
fx = -2(4 + 4x + x2)(2 + x)(-5 + x)

Multiply (4 + 4x + x2) * (2 + x)
fx = -2(4(2 + x) + 4x * (2 + x) + x2(2 + x))(-5 + x)
fx = -2((2 * 4 + x * 4) + 4x * (2 + x) + x2(2 + x))(-5 + x)
fx = -2((8 + 4x) + 4x * (2 + x) + x2(2 + x))(-5 + x)
fx = -2(8 + 4x + (2 * 4x + x * 4x) + x2(2 + x))(-5 + x)
fx = -2(8 + 4x + (8x + 4x2) + x2(2 + x))(-5 + x)
fx = -2(8 + 4x + 8x + 4x2 + (2 * x2 + x * x2))(-5 + x)
fx = -2(8 + 4x + 8x + 4x2 + (2x2 + x3))(-5 + x)

Combine like terms: 4x + 8x = 12x
fx = -2(8 + 12x + 4x2 + 2x2 + x3)(-5 + x)

Combine like terms: 4x2 + 2x2 = 6x2
fx = -2(8 + 12x + 6x2 + x3)(-5 + x)

Multiply (8 + 12x + 6x2 + x3) * (-5 + x)
fx = -2(8(-5 + x) + 12x * (-5 + x) + 6x2 * (-5 + x) + x3(-5 + x))
fx = -2((-5 * 8 + x * 8) + 12x * (-5 + x) + 6x2 * (-5 + x) + x3(-5 + x))
fx = -2((-40 + 8x) + 12x * (-5 + x) + 6x2 * (-5 + x) + x3(-5 + x))
fx = -2(-40 + 8x + (-5 * 12x + x * 12x) + 6x2 * (-5 + x) + x3(-5 + x))
fx = -2(-40 + 8x + (-60x + 12x2) + 6x2 * (-5 + x) + x3(-5 + x))
fx = -2(-40 + 8x + -60x + 12x2 + (-5 * 6x2 + x * 6x2) + x3(-5 + x))
fx = -2(-40 + 8x + -60x + 12x2 + (-30x2 + 6x3) + x3(-5 + x))
fx = -2(-40 + 8x + -60x + 12x2 + -30x2 + 6x3 + (-5 * x3 + x * x3))
fx = -2(-40 + 8x + -60x + 12x2 + -30x2 + 6x3 + (-5x3 + x4))

Combine like terms: 8x + -60x = -52x
fx = -2(-40 + -52x + 12x2 + -30x2 + 6x3 + -5x3 + x4)

Combine like terms: 12x2 + -30x2 = -18x2
fx = -2(-40 + -52x + -18x2 + 6x3 + -5x3 + x4)

Combine like terms: 6x3 + -5x3 = 1x3
fx = -2(-40 + -52x + -18x2 + 1x3 + x4)
fx = (-40 * -2 + -52x * -2 + -18x2 * -2 + 1x3 * -2 + x4 * -2)
fx = (80 + 104x + 36x2 + -2x3 + -2x4)

Solving
fx = 80 + 104x + 36x2 + -2x3 + -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 = 80x-1 + 104 + 36x + -2x2 + -2x3

Simplifying
f = 80x-1 + 104 + 36x + -2x2 + -2x3

Reorder the terms:
f = 104 + 80x-1 + 36x + -2x2 + -2x3

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