f(x)=(x+2)(x-3i)(x+3i)

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Solution for f(x)=(x+2)(x-3i)(x+3i) equation: 


Simplifying
f(x) = (x + 2)(x + -3i)(x + 3i)

Multiply f * x
fx = (x + 2)(x + -3i)(x + 3i)

Reorder the terms:
fx = (2 + x)(x + -3i)(x + 3i)

Reorder the terms:
fx = (2 + x)(-3i + x)(x + 3i)

Reorder the terms:
fx = (2 + x)(-3i + x)(3i + x)

Multiply (2 + x) * (-3i + x)
fx = (2(-3i + x) + x(-3i + x))(3i + x)
fx = ((-3i * 2 + x * 2) + x(-3i + x))(3i + x)
fx = ((-6i + 2x) + x(-3i + x))(3i + x)
fx = (-6i + 2x + (-3i * x + x * x))(3i + x)
fx = (-6i + 2x + (-3ix + x2))(3i + x)

Reorder the terms:
fx = (-6i + -3ix + 2x + x2)(3i + x)
fx = (-6i + -3ix + 2x + x2)(3i + x)

Multiply (-6i + -3ix + 2x + x2) * (3i + x)
fx = (-6i * (3i + x) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x))
fx = ((3i * -6i + x * -6i) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x))

Reorder the terms:
fx = ((-6ix + -18i2) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x))
fx = ((-6ix + -18i2) + -3ix * (3i + x) + 2x * (3i + x) + x2(3i + x))
fx = (-6ix + -18i2 + (3i * -3ix + x * -3ix) + 2x * (3i + x) + x2(3i + x))

Reorder the terms:
fx = (-6ix + -18i2 + (-3ix2 + -9i2x) + 2x * (3i + x) + x2(3i + x))
fx = (-6ix + -18i2 + (-3ix2 + -9i2x) + 2x * (3i + x) + x2(3i + x))
fx = (-6ix + -18i2 + -3ix2 + -9i2x + (3i * 2x + x * 2x) + x2(3i + x))
fx = (-6ix + -18i2 + -3ix2 + -9i2x + (6ix + 2x2) + x2(3i + x))
fx = (-6ix + -18i2 + -3ix2 + -9i2x + 6ix + 2x2 + (3i * x2 + x * x2))
fx = (-6ix + -18i2 + -3ix2 + -9i2x + 6ix + 2x2 + (3ix2 + x3))

Reorder the terms:
fx = (-6ix + 6ix + -3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3)

Combine like terms: -6ix + 6ix = 0
fx = (0 + -3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3)
fx = (-3ix2 + 3ix2 + -18i2 + -9i2x + 2x2 + x3)

Combine like terms: -3ix2 + 3ix2 = 0
fx = (0 + -18i2 + -9i2x + 2x2 + x3)
fx = (-18i2 + -9i2x + 2x2 + x3)

Solving
fx = -18i2 + -9i2x + 2x2 + 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 = -18i2x-1 + -9i2 + 2x + x2

Simplifying
f = -18i2x-1 + -9i2 + 2x + x2

Reorder the terms:
f = -9i2 + -18i2x-1 + 2x + x2

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