f(x)=(x+2)(x-9+4i)(x+9+4i)

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Solution for f(x)=(x+2)(x-9+4i)(x+9+4i) equation: 


Simplifying
f(x) = (x + 2)(x + -9 + 4i)(x + 9 + 4i)

Multiply f * x
fx = (x + 2)(x + -9 + 4i)(x + 9 + 4i)

Reorder the terms:
fx = (2 + x)(x + -9 + 4i)(x + 9 + 4i)

Reorder the terms:
fx = (2 + x)(-9 + 4i + x)(x + 9 + 4i)

Reorder the terms:
fx = (2 + x)(-9 + 4i + x)(9 + 4i + x)

Multiply (2 + x) * (-9 + 4i + x)
fx = (2(-9 + 4i + x) + x(-9 + 4i + x))(9 + 4i + x)
fx = ((-9 * 2 + 4i * 2 + x * 2) + x(-9 + 4i + x))(9 + 4i + x)
fx = ((-18 + 8i + 2x) + x(-9 + 4i + x))(9 + 4i + x)
fx = (-18 + 8i + 2x + (-9 * x + 4i * x + x * x))(9 + 4i + x)

Reorder the terms:
fx = (-18 + 8i + 2x + (4ix + -9x + x2))(9 + 4i + x)
fx = (-18 + 8i + 2x + (4ix + -9x + x2))(9 + 4i + x)

Reorder the terms:
fx = (-18 + 8i + 4ix + 2x + -9x + x2)(9 + 4i + x)

Combine like terms: 2x + -9x = -7x
fx = (-18 + 8i + 4ix + -7x + x2)(9 + 4i + x)

Multiply (-18 + 8i + 4ix + -7x + x2) * (9 + 4i + x)
fx = (-18(9 + 4i + x) + 8i * (9 + 4i + x) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = ((9 * -18 + 4i * -18 + x * -18) + 8i * (9 + 4i + x) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = ((-162 + -72i + -18x) + 8i * (9 + 4i + x) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + (9 * 8i + 4i * 8i + x * 8i) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))

Reorder the terms:
fx = (-162 + -72i + -18x + (72i + 8ix + 32i2) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + (72i + 8ix + 32i2) + 4ix * (9 + 4i + x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + (9 * 4ix + 4i * 4ix + x * 4ix) + -7x * (9 + 4i + x) + x2(9 + 4i + x))

Reorder the terms:
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + (36ix + 4ix2 + 16i2x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + (36ix + 4ix2 + 16i2x) + -7x * (9 + 4i + x) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + (9 * -7x + 4i * -7x + x * -7x) + x2(9 + 4i + x))

Reorder the terms:
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + (-28ix + -63x + -7x2) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + (-28ix + -63x + -7x2) + x2(9 + 4i + x))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + -28ix + -63x + -7x2 + (9 * x2 + 4i * x2 + x * x2))

Reorder the terms:
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + -28ix + -63x + -7x2 + (4ix2 + 9x2 + x3))
fx = (-162 + -72i + -18x + 72i + 8ix + 32i2 + 36ix + 4ix2 + 16i2x + -28ix + -63x + -7x2 + (4ix2 + 9x2 + x3))

Reorder the terms:
fx = (-162 + -72i + 72i + 8ix + 36ix + -28ix + 4ix2 + 4ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)

Combine like terms: -72i + 72i = 0
fx = (-162 + 0 + 8ix + 36ix + -28ix + 4ix2 + 4ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)
fx = (-162 + 8ix + 36ix + -28ix + 4ix2 + 4ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)

Combine like terms: 8ix + 36ix = 44ix
fx = (-162 + 44ix + -28ix + 4ix2 + 4ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)

Combine like terms: 44ix + -28ix = 16ix
fx = (-162 + 16ix + 4ix2 + 4ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)

Combine like terms: 4ix2 + 4ix2 = 8ix2
fx = (-162 + 16ix + 8ix2 + 32i2 + 16i2x + -18x + -63x + -7x2 + 9x2 + x3)

Combine like terms: -18x + -63x = -81x
fx = (-162 + 16ix + 8ix2 + 32i2 + 16i2x + -81x + -7x2 + 9x2 + x3)

Combine like terms: -7x2 + 9x2 = 2x2
fx = (-162 + 16ix + 8ix2 + 32i2 + 16i2x + -81x + 2x2 + x3)

Solving
fx = -162 + 16ix + 8ix2 + 32i2 + 16i2x + -81x + 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 = -162x-1 + 16i + 8ix + 32i2x-1 + 16i2 + -81 + 2x + x2

Simplifying
f = -162x-1 + 16i + 8ix + 32i2x-1 + 16i2 + -81 + 2x + x2

Reorder the terms:
f = -81 + 16i + 8ix + 16i2 + 32i2x-1 + -162x-1 + 2x + x2

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