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

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


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

Reorder the terms:
0 = [5 + -3i + x][x + -1(-5 + -3i)]
0 = [5 + -3i + x][x + (-5 * -1 + -3i * -1)]
0 = [5 + -3i + x][x + (5 + 3i)]

Reorder the terms:
0 = [5 + -3i + x][5 + 3i + x]

Multiply [5 + -3i + x] * [5 + 3i + x]
0 = [5[5 + 3i + x] + -3i * [5 + 3i + x] + x[5 + 3i + x]]
0 = [[5 * 5 + 3i * 5 + x * 5] + -3i * [5 + 3i + x] + x[5 + 3i + x]]
0 = [[25 + 15i + 5x] + -3i * [5 + 3i + x] + x[5 + 3i + x]]
0 = [25 + 15i + 5x + [5 * -3i + 3i * -3i + x * -3i] + x[5 + 3i + x]]

Reorder the terms:
0 = [25 + 15i + 5x + [-15i + -3ix + -9i2] + x[5 + 3i + x]]
0 = [25 + 15i + 5x + [-15i + -3ix + -9i2] + x[5 + 3i + x]]
0 = [25 + 15i + 5x + -15i + -3ix + -9i2 + [5 * x + 3i * x + x * x]]

Reorder the terms:
0 = [25 + 15i + 5x + -15i + -3ix + -9i2 + [3ix + 5x + x2]]
0 = [25 + 15i + 5x + -15i + -3ix + -9i2 + [3ix + 5x + x2]]

Reorder the terms:
0 = [25 + 15i + -15i + -3ix + 3ix + -9i2 + 5x + 5x + x2]

Combine like terms: 15i + -15i = 0
0 = [25 + 0 + -3ix + 3ix + -9i2 + 5x + 5x + x2]
0 = [25 + -3ix + 3ix + -9i2 + 5x + 5x + x2]

Combine like terms: -3ix + 3ix = 0
0 = [25 + 0 + -9i2 + 5x + 5x + x2]
0 = [25 + -9i2 + 5x + 5x + x2]

Combine like terms: 5x + 5x = 10x
0 = [25 + -9i2 + 10x + x2]

Solving
0 = 25 + -9i2 + 10x + x2

Solving for variable 'i'.

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

Add '9i2' to each side of the equation.
0 + 9i2 = 25 + -9i2 + 10x + 9i2 + x2
Remove the zero:
9i2 = 25 + -9i2 + 10x + 9i2 + x2

Reorder the terms:
9i2 = 25 + -9i2 + 9i2 + 10x + x2

Combine like terms: -9i2 + 9i2 = 0
9i2 = 25 + 0 + 10x + x2
9i2 = 25 + 10x + x2

Divide each side by '9'.
i2 = 2.777777778 + 1.111111111x + 0.1111111111x2

Simplifying
i2 = 2.777777778 + 1.111111111x + 0.1111111111x2

Reorder the terms:
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 2.777777778 + 1.111111111x + 0.1111111111x2 + -2.777777778 + -1.111111111x + -0.1111111111x2

Reorder the terms:
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 2.777777778 + -2.777777778 + 1.111111111x + -1.111111111x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: 2.777777778 + -2.777777778 = 0.000000000
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 0.000000000 + 1.111111111x + -1.111111111x + 0.1111111111x2 + -0.1111111111x2
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 1.111111111x + -1.111111111x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: 1.111111111x + -1.111111111x = 0.000000000
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2

Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000
-2.777777778 + i2 + -1.111111111x + -0.1111111111x2 = 0.0000000000

The solution to this equation could not be determined.

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