f(x)=(x+1)[x-(3-5i)][x-(3+5i)]

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Solution for f(x)=(x+1)[x-(3-5i)][x-(3+5i)] equation: 


Simplifying
f(x) = (x + 1)[x + -1(3 + -5i)][x + -1(3 + 5i)]

Multiply f * x
fx = (x + 1)[x + -1(3 + -5i)][x + -1(3 + 5i)]

Reorder the terms:
fx = (1 + x)[x + -1(3 + -5i)][x + -1(3 + 5i)]
fx = (1 + x)[x + (3 * -1 + -5i * -1)][x + -1(3 + 5i)]
fx = (1 + x)[x + (-3 + 5i)][x + -1(3 + 5i)]

Reorder the terms:
fx = (1 + x)[-3 + 5i + x][x + -1(3 + 5i)]
fx = (1 + x)[-3 + 5i + x][x + (3 * -1 + 5i * -1)]
fx = (1 + x)[-3 + 5i + x][x + (-3 + -5i)]

Reorder the terms:
fx = (1 + x)[-3 + 5i + x][-3 + -5i + x]

Multiply (1 + x) * [-3 + 5i + x]
fx = (1[-3 + 5i + x] + x[-3 + 5i + x])[-3 + -5i + x]
fx = ([-3 * 1 + 5i * 1 + x * 1] + x[-3 + 5i + x])[-3 + -5i + x]
fx = ([-3 + 5i + 1x] + x[-3 + 5i + x])[-3 + -5i + x]
fx = (-3 + 5i + 1x + [-3 * x + 5i * x + x * x])[-3 + -5i + x]

Reorder the terms:
fx = (-3 + 5i + 1x + [5ix + -3x + x2])[-3 + -5i + x]
fx = (-3 + 5i + 1x + [5ix + -3x + x2])[-3 + -5i + x]

Reorder the terms:
fx = (-3 + 5i + 5ix + 1x + -3x + x2)[-3 + -5i + x]

Combine like terms: 1x + -3x = -2x
fx = (-3 + 5i + 5ix + -2x + x2)[-3 + -5i + x]

Multiply (-3 + 5i + 5ix + -2x + x2) * [-3 + -5i + x]
fx = (-3[-3 + -5i + x] + 5i * [-3 + -5i + x] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = ([-3 * -3 + -5i * -3 + x * -3] + 5i * [-3 + -5i + x] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = ([9 + 15i + -3x] + 5i * [-3 + -5i + x] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + [-3 * 5i + -5i * 5i + x * 5i] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])

Reorder the terms:
fx = (9 + 15i + -3x + [-15i + 5ix + -25i2] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + [-15i + 5ix + -25i2] + 5ix * [-3 + -5i + x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + [-3 * 5ix + -5i * 5ix + x * 5ix] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])

Reorder the terms:
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + [-15ix + 5ix2 + -25i2x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + [-15ix + 5ix2 + -25i2x] + -2x * [-3 + -5i + x] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + [-3 * -2x + -5i * -2x + x * -2x] + x2[-3 + -5i + x])

Reorder the terms:
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + [10ix + 6x + -2x2] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + [10ix + 6x + -2x2] + x2[-3 + -5i + x])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + 10ix + 6x + -2x2 + [-3 * x2 + -5i * x2 + x * x2])

Reorder the terms:
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + 10ix + 6x + -2x2 + [-5ix2 + -3x2 + x3])
fx = (9 + 15i + -3x + -15i + 5ix + -25i2 + -15ix + 5ix2 + -25i2x + 10ix + 6x + -2x2 + [-5ix2 + -3x2 + x3])

Reorder the terms:
fx = (9 + 15i + -15i + 5ix + -15ix + 10ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: 15i + -15i = 0
fx = (9 + 0 + 5ix + -15ix + 10ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + 5ix + -15ix + 10ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: 5ix + -15ix = -10ix
fx = (9 + -10ix + 10ix + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -10ix + 10ix = 0
fx = (9 + 0 + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + 5ix2 + -5ix2 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: 5ix2 + -5ix2 = 0
fx = (9 + 0 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)
fx = (9 + -25i2 + -25i2x + -3x + 6x + -2x2 + -3x2 + x3)

Combine like terms: -3x + 6x = 3x
fx = (9 + -25i2 + -25i2x + 3x + -2x2 + -3x2 + x3)

Combine like terms: -2x2 + -3x2 = -5x2
fx = (9 + -25i2 + -25i2x + 3x + -5x2 + x3)

Solving
fx = 9 + -25i2 + -25i2x + 3x + -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 = 9x-1 + -25i2x-1 + -25i2 + 3 + -5x + x2

Simplifying
f = 9x-1 + -25i2x-1 + -25i2 + 3 + -5x + x2

Reorder the terms:
f = 3 + -25i2 + -25i2x-1 + 9x-1 + -5x + x2

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