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

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


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

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

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

Multiply (-4 + 3i + x) * (-4 + -3i + x)
(-4(-4 + -3i + x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x)) = y
((-4 * -4 + -3i * -4 + x * -4) + 3i * (-4 + -3i + x) + x(-4 + -3i + x)) = y
((16 + 12i + -4x) + 3i * (-4 + -3i + x) + x(-4 + -3i + x)) = y
(16 + 12i + -4x + (-4 * 3i + -3i * 3i + x * 3i) + x(-4 + -3i + x)) = y

Reorder the terms:
(16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x)) = y
(16 + 12i + -4x + (-12i + 3ix + -9i2) + x(-4 + -3i + x)) = y
(16 + 12i + -4x + -12i + 3ix + -9i2 + (-4 * x + -3i * x + x * x)) = y

Reorder the terms:
(16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2)) = y
(16 + 12i + -4x + -12i + 3ix + -9i2 + (-3ix + -4x + x2)) = y

Reorder the terms:
(16 + 12i + -12i + 3ix + -3ix + -9i2 + -4x + -4x + x2) = y

Combine like terms: 12i + -12i = 0
(16 + 0 + 3ix + -3ix + -9i2 + -4x + -4x + x2) = y
(16 + 3ix + -3ix + -9i2 + -4x + -4x + x2) = y

Combine like terms: 3ix + -3ix = 0
(16 + 0 + -9i2 + -4x + -4x + x2) = y
(16 + -9i2 + -4x + -4x + x2) = y

Combine like terms: -4x + -4x = -8x
(16 + -9i2 + -8x + x2) = y

Solving
16 + -9i2 + -8x + x2 = y

Solving for variable 'i'.

Move all terms containing i to the left, all other terms to the right.

Add '-16' to each side of the equation.
16 + -9i2 + -8x + -16 + x2 = -16 + y

Reorder the terms:
16 + -16 + -9i2 + -8x + x2 = -16 + y

Combine like terms: 16 + -16 = 0
0 + -9i2 + -8x + x2 = -16 + y
-9i2 + -8x + x2 = -16 + y

Add '8x' to each side of the equation.
-9i2 + -8x + 8x + x2 = -16 + 8x + y

Combine like terms: -8x + 8x = 0
-9i2 + 0 + x2 = -16 + 8x + y
-9i2 + x2 = -16 + 8x + y

Add '-1x2' to each side of the equation.
-9i2 + x2 + -1x2 = -16 + 8x + -1x2 + y

Combine like terms: x2 + -1x2 = 0
-9i2 + 0 = -16 + 8x + -1x2 + y
-9i2 = -16 + 8x + -1x2 + y

Divide each side by '-9'.
i2 = 1.777777778 + -0.8888888889x + 0.1111111111x2 + -0.1111111111y

Simplifying
i2 = 1.777777778 + -0.8888888889x + 0.1111111111x2 + -0.1111111111y

Reorder the terms:
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 1.777777778 + -0.8888888889x + 0.1111111111x2 + -0.1111111111y + -1.777777778 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y

Reorder the terms:
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 1.777777778 + -1.777777778 + -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 + -0.1111111111y + 0.1111111111y

Combine like terms: 1.777777778 + -1.777777778 = 0.000000000
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 0.000000000 + -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 + -0.1111111111y + 0.1111111111y
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = -0.8888888889x + 0.8888888889x + 0.1111111111x2 + -0.1111111111x2 + -0.1111111111y + 0.1111111111y

Combine like terms: -0.8888888889x + 0.8888888889x = 0.0000000000
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 0.0000000000 + 0.1111111111x2 + -0.1111111111x2 + -0.1111111111y + 0.1111111111y
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 0.1111111111x2 + -0.1111111111x2 + -0.1111111111y + 0.1111111111y

Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 0.0000000000 + -0.1111111111y + 0.1111111111y
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = -0.1111111111y + 0.1111111111y

Combine like terms: -0.1111111111y + 0.1111111111y = 0.0000000000
-1.777777778 + i2 + 0.8888888889x + -0.1111111111x2 + 0.1111111111y = 0.0000000000

The solution to this equation could not be determined.

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