x=(x+3)(x+4i)

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Solution for x=(x+3)(x+4i) equation: 


Simplifying
x = (x + 3)(x + 4i)

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

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

Multiply (3 + x) * (4i + x)
x = (3(4i + x) + x(4i + x))
x = ((4i * 3 + x * 3) + x(4i + x))
x = ((12i + 3x) + x(4i + x))
x = (12i + 3x + (4i * x + x * x))
x = (12i + 3x + (4ix + x2))

Reorder the terms:
x = (12i + 4ix + 3x + x2)
x = (12i + 4ix + 3x + x2)

Solving
x = 12i + 4ix + 3x + x2

Solving for variable 'x'.

Reorder the terms:
-12i + -4ix + x + -3x + -1x2 = 12i + 4ix + 3x + x2 + -12i + -4ix + -3x + -1x2

Combine like terms: x + -3x = -2x
-12i + -4ix + -2x + -1x2 = 12i + 4ix + 3x + x2 + -12i + -4ix + -3x + -1x2

Reorder the terms:
-12i + -4ix + -2x + -1x2 = 12i + -12i + 4ix + -4ix + 3x + -3x + x2 + -1x2

Combine like terms: 12i + -12i = 0
-12i + -4ix + -2x + -1x2 = 0 + 4ix + -4ix + 3x + -3x + x2 + -1x2
-12i + -4ix + -2x + -1x2 = 4ix + -4ix + 3x + -3x + x2 + -1x2

Combine like terms: 4ix + -4ix = 0
-12i + -4ix + -2x + -1x2 = 0 + 3x + -3x + x2 + -1x2
-12i + -4ix + -2x + -1x2 = 3x + -3x + x2 + -1x2

Combine like terms: 3x + -3x = 0
-12i + -4ix + -2x + -1x2 = 0 + x2 + -1x2
-12i + -4ix + -2x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-12i + -4ix + -2x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(12i + 4ix + 2x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(12i + 4ix + 2x + x2)' equal to zero and attempt to solve:

Simplifying
12i + 4ix + 2x + x2 = 0

Solving
12i + 4ix + 2x + x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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