(X-9)(x+(1+2i))(x-(1-2i))=0

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Solution for (X-9)(x+(1+2i))(x-(1-2i))=0 equation: 


Simplifying
(X + -9)(x + (1 + 2i))(x + -1(1 + -2i)) = 0

Reorder the terms:
(-9 + X)(x + (1 + 2i))(x + -1(1 + -2i)) = 0

Remove parenthesis around (1 + 2i)
(-9 + X)(x + 1 + 2i)(x + -1(1 + -2i)) = 0

Reorder the terms:
(-9 + X)(1 + 2i + x)(x + -1(1 + -2i)) = 0
(-9 + X)(1 + 2i + x)(x + (1 * -1 + -2i * -1)) = 0
(-9 + X)(1 + 2i + x)(x + (-1 + 2i)) = 0

Reorder the terms:
(-9 + X)(1 + 2i + x)(-1 + 2i + x) = 0

Multiply (-9 + X) * (1 + 2i + x)
(-9(1 + 2i + x) + X(1 + 2i + x))(-1 + 2i + x) = 0
((1 * -9 + 2i * -9 + x * -9) + X(1 + 2i + x))(-1 + 2i + x) = 0
((-9 + -18i + -9x) + X(1 + 2i + x))(-1 + 2i + x) = 0
(-9 + -18i + -9x + (1 * X + 2i * X + x * X))(-1 + 2i + x) = 0
(-9 + -18i + -9x + (1X + 2iX + xX))(-1 + 2i + x) = 0

Reorder the terms:
(-9 + 1X + -18i + 2iX + -9x + xX)(-1 + 2i + x) = 0
(-9 + 1X + -18i + 2iX + -9x + xX)(-1 + 2i + x) = 0

Multiply (-9 + 1X + -18i + 2iX + -9x + xX) * (-1 + 2i + x)
(-9(-1 + 2i + x) + 1X * (-1 + 2i + x) + -18i * (-1 + 2i + x) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
((-1 * -9 + 2i * -9 + x * -9) + 1X * (-1 + 2i + x) + -18i * (-1 + 2i + x) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
((9 + -18i + -9x) + 1X * (-1 + 2i + x) + -18i * (-1 + 2i + x) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + (-1 * 1X + 2i * 1X + x * 1X) + -18i * (-1 + 2i + x) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + (-1X + 2iX + 1xX) + -18i * (-1 + 2i + x) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + (-1 * -18i + 2i * -18i + x * -18i) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0

Reorder the terms:
(9 + -18i + -9x + -1X + 2iX + 1xX + (18i + -18ix + -36i2) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + (18i + -18ix + -36i2) + 2iX * (-1 + 2i + x) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + (-1 * 2iX + 2i * 2iX + x * 2iX) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0

Reorder the terms:
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + (-2iX + 2ixX + 4i2X) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + (-2iX + 2ixX + 4i2X) + -9x * (-1 + 2i + x) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + (-1 * -9x + 2i * -9x + x * -9x) + xX(-1 + 2i + x)) = 0

Reorder the terms:
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + (-18ix + 9x + -9x2) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + (-18ix + 9x + -9x2) + xX(-1 + 2i + x)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + -18ix + 9x + -9x2 + (-1 * xX + 2i * xX + x * xX)) = 0

Reorder the terms:
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + -18ix + 9x + -9x2 + (2ixX + -1xX + x2X)) = 0
(9 + -18i + -9x + -1X + 2iX + 1xX + 18i + -18ix + -36i2 + -2iX + 2ixX + 4i2X + -18ix + 9x + -9x2 + (2ixX + -1xX + x2X)) = 0

Reorder the terms:
(9 + -1X + -18i + 18i + 2iX + -2iX + -18ix + -18ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: -18i + 18i = 0
(9 + -1X + 0 + 2iX + -2iX + -18ix + -18ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0
(9 + -1X + 2iX + -2iX + -18ix + -18ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: 2iX + -2iX = 0
(9 + -1X + 0 + -18ix + -18ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0
(9 + -1X + -18ix + -18ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: -18ix + -18ix = -36ix
(9 + -1X + -36ix + 2ixX + 2ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: 2ixX + 2ixX = 4ixX
(9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x + 9x + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: -9x + 9x = 0
(9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + 0 + 1xX + -1xX + -9x2 + x2X) = 0
(9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + 1xX + -1xX + -9x2 + x2X) = 0

Combine like terms: 1xX + -1xX = 0
(9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + 0 + -9x2 + x2X) = 0
(9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X) = 0

Solving
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0

Solving for variable 'X'.

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

Add '-9' to each side of the equation.
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + -9 + x2X = 0 + -9

Reorder the terms:
9 + -9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + -9
-1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + -9

Combine like terms: 0 + -9 = -9
-1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9

Add '36ix' to each side of the equation.
-1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + 36ix + x2X = -9 + 36ix

Reorder the terms:
-1X + -36ix + 36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9 + 36ix

Combine like terms: -36ix + 36ix = 0
-1X + 0 + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9 + 36ix
-1X + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9 + 36ix

Add '36i2' to each side of the equation.
-1X + 4ixX + -36i2 + 4i2X + -9x2 + 36i2 + x2X = -9 + 36ix + 36i2

Reorder the terms:
-1X + 4ixX + -36i2 + 36i2 + 4i2X + -9x2 + x2X = -9 + 36ix + 36i2

Combine like terms: -36i2 + 36i2 = 0
-1X + 4ixX + 0 + 4i2X + -9x2 + x2X = -9 + 36ix + 36i2
-1X + 4ixX + 4i2X + -9x2 + x2X = -9 + 36ix + 36i2

Add '9x2' to each side of the equation.
-1X + 4ixX + 4i2X + -9x2 + 9x2 + x2X = -9 + 36ix + 36i2 + 9x2

Combine like terms: -9x2 + 9x2 = 0
-1X + 4ixX + 4i2X + 0 + x2X = -9 + 36ix + 36i2 + 9x2
-1X + 4ixX + 4i2X + x2X = -9 + 36ix + 36i2 + 9x2

Reorder the terms:
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9 + 36ix + 36i2 + 9x2 + 9 + -36ix + -36i2 + -9x2

Reorder the terms:
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = -9 + 9 + 36ix + -36ix + 36i2 + -36i2 + 9x2 + -9x2

Combine like terms: -9 + 9 = 0
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + 36ix + -36ix + 36i2 + -36i2 + 9x2 + -9x2
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 36ix + -36ix + 36i2 + -36i2 + 9x2 + -9x2

Combine like terms: 36ix + -36ix = 0
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + 36i2 + -36i2 + 9x2 + -9x2
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 36i2 + -36i2 + 9x2 + -9x2

Combine like terms: 36i2 + -36i2 = 0
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0 + 9x2 + -9x2
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
9 + -1X + -36ix + 4ixX + -36i2 + 4i2X + -9x2 + x2X = 0

The solution to this equation could not be determined.

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