f(x)=(x+3)(x-5x-5i)(x-5x+5i)

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Solution for f(x)=(x+3)(x-5x-5i)(x-5x+5i) equation: 


Simplifying
f(x) = (x + 3)(x + -5x + -5i)(x + -5x + 5i)

Multiply f * x
fx = (x + 3)(x + -5x + -5i)(x + -5x + 5i)

Reorder the terms:
fx = (3 + x)(x + -5x + -5i)(x + -5x + 5i)

Reorder the terms:
fx = (3 + x)(-5i + x + -5x)(x + -5x + 5i)

Combine like terms: x + -5x = -4x
fx = (3 + x)(-5i + -4x)(x + -5x + 5i)

Reorder the terms:
fx = (3 + x)(-5i + -4x)(5i + x + -5x)

Combine like terms: x + -5x = -4x
fx = (3 + x)(-5i + -4x)(5i + -4x)

Multiply (3 + x) * (-5i + -4x)
fx = (3(-5i + -4x) + x(-5i + -4x))(5i + -4x)
fx = ((-5i * 3 + -4x * 3) + x(-5i + -4x))(5i + -4x)
fx = ((-15i + -12x) + x(-5i + -4x))(5i + -4x)
fx = (-15i + -12x + (-5i * x + -4x * x))(5i + -4x)
fx = (-15i + -12x + (-5ix + -4x2))(5i + -4x)

Reorder the terms:
fx = (-15i + -5ix + -12x + -4x2)(5i + -4x)
fx = (-15i + -5ix + -12x + -4x2)(5i + -4x)

Multiply (-15i + -5ix + -12x + -4x2) * (5i + -4x)
fx = (-15i * (5i + -4x) + -5ix * (5i + -4x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))
fx = ((5i * -15i + -4x * -15i) + -5ix * (5i + -4x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))

Reorder the terms:
fx = ((60ix + -75i2) + -5ix * (5i + -4x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))
fx = ((60ix + -75i2) + -5ix * (5i + -4x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))
fx = (60ix + -75i2 + (5i * -5ix + -4x * -5ix) + -12x * (5i + -4x) + -4x2 * (5i + -4x))

Reorder the terms:
fx = (60ix + -75i2 + (20ix2 + -25i2x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))
fx = (60ix + -75i2 + (20ix2 + -25i2x) + -12x * (5i + -4x) + -4x2 * (5i + -4x))
fx = (60ix + -75i2 + 20ix2 + -25i2x + (5i * -12x + -4x * -12x) + -4x2 * (5i + -4x))
fx = (60ix + -75i2 + 20ix2 + -25i2x + (-60ix + 48x2) + -4x2 * (5i + -4x))
fx = (60ix + -75i2 + 20ix2 + -25i2x + -60ix + 48x2 + (5i * -4x2 + -4x * -4x2))
fx = (60ix + -75i2 + 20ix2 + -25i2x + -60ix + 48x2 + (-20ix2 + 16x3))

Reorder the terms:
fx = (60ix + -60ix + 20ix2 + -20ix2 + -75i2 + -25i2x + 48x2 + 16x3)

Combine like terms: 60ix + -60ix = 0
fx = (0 + 20ix2 + -20ix2 + -75i2 + -25i2x + 48x2 + 16x3)
fx = (20ix2 + -20ix2 + -75i2 + -25i2x + 48x2 + 16x3)

Combine like terms: 20ix2 + -20ix2 = 0
fx = (0 + -75i2 + -25i2x + 48x2 + 16x3)
fx = (-75i2 + -25i2x + 48x2 + 16x3)

Solving
fx = -75i2 + -25i2x + 48x2 + 16x3

Solving for variable 'f'.

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

Divide each side by 'x'.
f = -75i2x-1 + -25i2 + 48x + 16x2

Simplifying
f = -75i2x-1 + -25i2 + 48x + 16x2

Reorder the terms:
f = -25i2 + -75i2x-1 + 48x + 16x2

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