(3+i)(x+yi)(3+4i)=3+9i

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Solution for (3+i)(x+yi)(3+4i)=3+9i equation: 


Simplifying
(3 + i)(x + yi)(3 + 4i) = 3 + 9i

Reorder the terms:
(3 + i)(iy + x)(3 + 4i) = 3 + 9i

Multiply (3 + i) * (iy + x)
(3(iy + x) + i(iy + x))(3 + 4i) = 3 + 9i
((iy * 3 + x * 3) + i(iy + x))(3 + 4i) = 3 + 9i
((3iy + 3x) + i(iy + x))(3 + 4i) = 3 + 9i
(3iy + 3x + (iy * i + x * i))(3 + 4i) = 3 + 9i

Reorder the terms:
(3iy + 3x + (ix + i2y))(3 + 4i) = 3 + 9i
(3iy + 3x + (ix + i2y))(3 + 4i) = 3 + 9i

Reorder the terms:
(ix + 3iy + i2y + 3x)(3 + 4i) = 3 + 9i
(ix + 3iy + i2y + 3x)(3 + 4i) = 3 + 9i

Multiply (ix + 3iy + i2y + 3x) * (3 + 4i)
(ix(3 + 4i) + 3iy * (3 + 4i) + i2y(3 + 4i) + 3x * (3 + 4i)) = 3 + 9i
((3 * ix + 4i * ix) + 3iy * (3 + 4i) + i2y(3 + 4i) + 3x * (3 + 4i)) = 3 + 9i
((3ix + 4i2x) + 3iy * (3 + 4i) + i2y(3 + 4i) + 3x * (3 + 4i)) = 3 + 9i
(3ix + 4i2x + (3 * 3iy + 4i * 3iy) + i2y(3 + 4i) + 3x * (3 + 4i)) = 3 + 9i
(3ix + 4i2x + (9iy + 12i2y) + i2y(3 + 4i) + 3x * (3 + 4i)) = 3 + 9i
(3ix + 4i2x + 9iy + 12i2y + (3 * i2y + 4i * i2y) + 3x * (3 + 4i)) = 3 + 9i
(3ix + 4i2x + 9iy + 12i2y + (3i2y + 4i3y) + 3x * (3 + 4i)) = 3 + 9i
(3ix + 4i2x + 9iy + 12i2y + 3i2y + 4i3y + (3 * 3x + 4i * 3x)) = 3 + 9i

Reorder the terms:
(3ix + 4i2x + 9iy + 12i2y + 3i2y + 4i3y + (12ix + 9x)) = 3 + 9i
(3ix + 4i2x + 9iy + 12i2y + 3i2y + 4i3y + (12ix + 9x)) = 3 + 9i

Reorder the terms:
(3ix + 12ix + 9iy + 4i2x + 12i2y + 3i2y + 4i3y + 9x) = 3 + 9i

Combine like terms: 3ix + 12ix = 15ix
(15ix + 9iy + 4i2x + 12i2y + 3i2y + 4i3y + 9x) = 3 + 9i

Combine like terms: 12i2y + 3i2y = 15i2y
(15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x) = 3 + 9i

Solving
15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 3 + 9i

Solving for variable 'i'.

Reorder the terms:
-3 + -9i + 15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 3 + 9i + -3 + -9i

Reorder the terms:
-3 + -9i + 15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 3 + -3 + 9i + -9i

Combine like terms: 3 + -3 = 0
-3 + -9i + 15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 0 + 9i + -9i
-3 + -9i + 15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 9i + -9i

Combine like terms: 9i + -9i = 0
-3 + -9i + 15ix + 9iy + 4i2x + 15i2y + 4i3y + 9x = 0

The solution to this equation could not be determined.

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