f(x)=(x+4)(x-8)(2+5i)(2-5i)

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Solution for f(x)=(x+4)(x-8)(2+5i)(2-5i) equation: 


Simplifying
f(x) = (x + 4)(x + -8)(2 + 5i)(2 + -5i)

Multiply f * x
fx = (x + 4)(x + -8)(2 + 5i)(2 + -5i)

Reorder the terms:
fx = (4 + x)(x + -8)(2 + 5i)(2 + -5i)

Reorder the terms:
fx = (4 + x)(-8 + x)(2 + 5i)(2 + -5i)

Multiply (4 + x) * (-8 + x)
fx = (4(-8 + x) + x(-8 + x))(2 + 5i)(2 + -5i)
fx = ((-8 * 4 + x * 4) + x(-8 + x))(2 + 5i)(2 + -5i)
fx = ((-32 + 4x) + x(-8 + x))(2 + 5i)(2 + -5i)
fx = (-32 + 4x + (-8 * x + x * x))(2 + 5i)(2 + -5i)
fx = (-32 + 4x + (-8x + x2))(2 + 5i)(2 + -5i)

Combine like terms: 4x + -8x = -4x
fx = (-32 + -4x + x2)(2 + 5i)(2 + -5i)

Multiply (-32 + -4x + x2) * (2 + 5i)
fx = (-32(2 + 5i) + -4x * (2 + 5i) + x2(2 + 5i))(2 + -5i)
fx = ((2 * -32 + 5i * -32) + -4x * (2 + 5i) + x2(2 + 5i))(2 + -5i)
fx = ((-64 + -160i) + -4x * (2 + 5i) + x2(2 + 5i))(2 + -5i)
fx = (-64 + -160i + (2 * -4x + 5i * -4x) + x2(2 + 5i))(2 + -5i)

Reorder the terms:
fx = (-64 + -160i + (-20ix + -8x) + x2(2 + 5i))(2 + -5i)
fx = (-64 + -160i + (-20ix + -8x) + x2(2 + 5i))(2 + -5i)
fx = (-64 + -160i + -20ix + -8x + (2 * x2 + 5i * x2))(2 + -5i)

Reorder the terms:
fx = (-64 + -160i + -20ix + -8x + (5ix2 + 2x2))(2 + -5i)
fx = (-64 + -160i + -20ix + -8x + (5ix2 + 2x2))(2 + -5i)

Reorder the terms:
fx = (-64 + -160i + -20ix + 5ix2 + -8x + 2x2)(2 + -5i)
fx = (-64 + -160i + -20ix + 5ix2 + -8x + 2x2)(2 + -5i)

Multiply (-64 + -160i + -20ix + 5ix2 + -8x + 2x2) * (2 + -5i)
fx = (-64(2 + -5i) + -160i * (2 + -5i) + -20ix * (2 + -5i) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = ((2 * -64 + -5i * -64) + -160i * (2 + -5i) + -20ix * (2 + -5i) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = ((-128 + 320i) + -160i * (2 + -5i) + -20ix * (2 + -5i) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + (2 * -160i + -5i * -160i) + -20ix * (2 + -5i) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + (-320i + 800i2) + -20ix * (2 + -5i) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + (2 * -20ix + -5i * -20ix) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + (-40ix + 100i2x) + 5ix2 * (2 + -5i) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + (2 * 5ix2 + -5i * 5ix2) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + (10ix2 + -25i2x2) + -8x * (2 + -5i) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + (2 * -8x + -5i * -8x) + 2x2 * (2 + -5i))

Reorder the terms:
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + (40ix + -16x) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + (40ix + -16x) + 2x2 * (2 + -5i))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + 40ix + -16x + (2 * 2x2 + -5i * 2x2))

Reorder the terms:
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + 40ix + -16x + (-10ix2 + 4x2))
fx = (-128 + 320i + -320i + 800i2 + -40ix + 100i2x + 10ix2 + -25i2x2 + 40ix + -16x + (-10ix2 + 4x2))

Reorder the terms:
fx = (-128 + 320i + -320i + -40ix + 40ix + 10ix2 + -10ix2 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)

Combine like terms: 320i + -320i = 0
fx = (-128 + 0 + -40ix + 40ix + 10ix2 + -10ix2 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)
fx = (-128 + -40ix + 40ix + 10ix2 + -10ix2 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)

Combine like terms: -40ix + 40ix = 0
fx = (-128 + 0 + 10ix2 + -10ix2 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)
fx = (-128 + 10ix2 + -10ix2 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)

Combine like terms: 10ix2 + -10ix2 = 0
fx = (-128 + 0 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)
fx = (-128 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2)

Solving
fx = -128 + 800i2 + 100i2x + -25i2x2 + -16x + 4x2

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -128x-1 + 800i2x-1 + 100i2 + -25i2x + -16 + 4x

Simplifying
f = -128x-1 + 800i2x-1 + 100i2 + -25i2x + -16 + 4x

Reorder the terms:
f = -16 + 100i2 + 800i2x-1 + -25i2x + -128x-1 + 4x

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