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

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


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

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

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

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

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

Multiply (-5 + x) * (-5i + x)
fx = (-5(-5i + x) + x(-5i + x))(5i + x)
fx = ((-5i * -5 + x * -5) + x(-5i + x))(5i + x)
fx = ((25i + -5x) + x(-5i + x))(5i + x)
fx = (25i + -5x + (-5i * x + x * x))(5i + x)
fx = (25i + -5x + (-5ix + x2))(5i + x)

Reorder the terms:
fx = (25i + -5ix + -5x + x2)(5i + x)
fx = (25i + -5ix + -5x + x2)(5i + x)

Multiply (25i + -5ix + -5x + x2) * (5i + x)
fx = (25i * (5i + x) + -5ix * (5i + x) + -5x * (5i + x) + x2(5i + x))
fx = ((5i * 25i + x * 25i) + -5ix * (5i + x) + -5x * (5i + x) + x2(5i + x))

Reorder the terms:
fx = ((25ix + 125i2) + -5ix * (5i + x) + -5x * (5i + x) + x2(5i + x))
fx = ((25ix + 125i2) + -5ix * (5i + x) + -5x * (5i + x) + x2(5i + x))
fx = (25ix + 125i2 + (5i * -5ix + x * -5ix) + -5x * (5i + x) + x2(5i + x))

Reorder the terms:
fx = (25ix + 125i2 + (-5ix2 + -25i2x) + -5x * (5i + x) + x2(5i + x))
fx = (25ix + 125i2 + (-5ix2 + -25i2x) + -5x * (5i + x) + x2(5i + x))
fx = (25ix + 125i2 + -5ix2 + -25i2x + (5i * -5x + x * -5x) + x2(5i + x))
fx = (25ix + 125i2 + -5ix2 + -25i2x + (-25ix + -5x2) + x2(5i + x))
fx = (25ix + 125i2 + -5ix2 + -25i2x + -25ix + -5x2 + (5i * x2 + x * x2))
fx = (25ix + 125i2 + -5ix2 + -25i2x + -25ix + -5x2 + (5ix2 + x3))

Reorder the terms:
fx = (25ix + -25ix + -5ix2 + 5ix2 + 125i2 + -25i2x + -5x2 + x3)

Combine like terms: 25ix + -25ix = 0
fx = (0 + -5ix2 + 5ix2 + 125i2 + -25i2x + -5x2 + x3)
fx = (-5ix2 + 5ix2 + 125i2 + -25i2x + -5x2 + x3)

Combine like terms: -5ix2 + 5ix2 = 0
fx = (0 + 125i2 + -25i2x + -5x2 + x3)
fx = (125i2 + -25i2x + -5x2 + x3)

Solving
fx = 125i2 + -25i2x + -5x2 + x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = 125i2x-1 + -25i2 + -5x + x2

Simplifying
f = 125i2x-1 + -25i2 + -5x + x2

Reorder the terms:
f = -25i2 + 125i2x-1 + -5x + x2

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