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

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


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

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

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

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

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

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

Multiply (-2 + x) * (-5 + x)
fx = (-2(-5 + x) + x(-5 + x))(5i + x)(-5i + x)
fx = ((-5 * -2 + x * -2) + x(-5 + x))(5i + x)(-5i + x)
fx = ((10 + -2x) + x(-5 + x))(5i + x)(-5i + x)
fx = (10 + -2x + (-5 * x + x * x))(5i + x)(-5i + x)
fx = (10 + -2x + (-5x + x2))(5i + x)(-5i + x)

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

Multiply (10 + -7x + x2) * (5i + x)
fx = (10(5i + x) + -7x * (5i + x) + x2(5i + x))(-5i + x)
fx = ((5i * 10 + x * 10) + -7x * (5i + x) + x2(5i + x))(-5i + x)
fx = ((50i + 10x) + -7x * (5i + x) + x2(5i + x))(-5i + x)
fx = (50i + 10x + (5i * -7x + x * -7x) + x2(5i + x))(-5i + x)
fx = (50i + 10x + (-35ix + -7x2) + x2(5i + x))(-5i + x)
fx = (50i + 10x + -35ix + -7x2 + (5i * x2 + x * x2))(-5i + x)
fx = (50i + 10x + -35ix + -7x2 + (5ix2 + x3))(-5i + x)

Reorder the terms:
fx = (50i + -35ix + 5ix2 + 10x + -7x2 + x3)(-5i + x)
fx = (50i + -35ix + 5ix2 + 10x + -7x2 + x3)(-5i + x)

Multiply (50i + -35ix + 5ix2 + 10x + -7x2 + x3) * (-5i + x)
fx = (50i * (-5i + x) + -35ix * (-5i + x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = ((-5i * 50i + x * 50i) + -35ix * (-5i + x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))

Reorder the terms:
fx = ((50ix + -250i2) + -35ix * (-5i + x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = ((50ix + -250i2) + -35ix * (-5i + x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + (-5i * -35ix + x * -35ix) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))

Reorder the terms:
fx = (50ix + -250i2 + (-35ix2 + 175i2x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + (-35ix2 + 175i2x) + 5ix2 * (-5i + x) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + (-5i * 5ix2 + x * 5ix2) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))

Reorder the terms:
fx = (50ix + -250i2 + -35ix2 + 175i2x + (5ix3 + -25i2x2) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + (5ix3 + -25i2x2) + 10x * (-5i + x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + (-5i * 10x + x * 10x) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + (-50ix + 10x2) + -7x2 * (-5i + x) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + -50ix + 10x2 + (-5i * -7x2 + x * -7x2) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + -50ix + 10x2 + (35ix2 + -7x3) + x3(-5i + x))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + -50ix + 10x2 + 35ix2 + -7x3 + (-5i * x3 + x * x3))
fx = (50ix + -250i2 + -35ix2 + 175i2x + 5ix3 + -25i2x2 + -50ix + 10x2 + 35ix2 + -7x3 + (-5ix3 + x4))

Reorder the terms:
fx = (50ix + -50ix + -35ix2 + 35ix2 + 5ix3 + -5ix3 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)

Combine like terms: 50ix + -50ix = 0
fx = (0 + -35ix2 + 35ix2 + 5ix3 + -5ix3 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)
fx = (-35ix2 + 35ix2 + 5ix3 + -5ix3 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)

Combine like terms: -35ix2 + 35ix2 = 0
fx = (0 + 5ix3 + -5ix3 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)
fx = (5ix3 + -5ix3 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)

Combine like terms: 5ix3 + -5ix3 = 0
fx = (0 + -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)
fx = (-250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4)

Solving
fx = -250i2 + 175i2x + -25i2x2 + 10x2 + -7x3 + x4

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -250i2x-1 + 175i2 + -25i2x + 10x + -7x2 + x3

Simplifying
f = -250i2x-1 + 175i2 + -25i2x + 10x + -7x2 + x3

Reorder the terms:
f = 175i2 + -250i2x-1 + -25i2x + 10x + -7x2 + x3

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