(x+2)(x-9-4i)(x-9+4i)=0

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Solution for (x+2)(x-9-4i)(x-9+4i)=0 equation:


Simplifying
(x + 2)(x + -9 + -4i)(x + -9 + 4i) = 0

Reorder the terms:
(2 + x)(x + -9 + -4i)(x + -9 + 4i) = 0

Reorder the terms:
(2 + x)(-9 + -4i + x)(x + -9 + 4i) = 0

Reorder the terms:
(2 + x)(-9 + -4i + x)(-9 + 4i + x) = 0

Multiply (2 + x) * (-9 + -4i + x)
(2(-9 + -4i + x) + x(-9 + -4i + x))(-9 + 4i + x) = 0
((-9 * 2 + -4i * 2 + x * 2) + x(-9 + -4i + x))(-9 + 4i + x) = 0
((-18 + -8i + 2x) + x(-9 + -4i + x))(-9 + 4i + x) = 0
(-18 + -8i + 2x + (-9 * x + -4i * x + x * x))(-9 + 4i + x) = 0

Reorder the terms:
(-18 + -8i + 2x + (-4ix + -9x + x2))(-9 + 4i + x) = 0
(-18 + -8i + 2x + (-4ix + -9x + x2))(-9 + 4i + x) = 0

Reorder the terms:
(-18 + -8i + -4ix + 2x + -9x + x2)(-9 + 4i + x) = 0

Combine like terms: 2x + -9x = -7x
(-18 + -8i + -4ix + -7x + x2)(-9 + 4i + x) = 0

Multiply (-18 + -8i + -4ix + -7x + x2) * (-9 + 4i + x)
(-18(-9 + 4i + x) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
((-9 * -18 + 4i * -18 + x * -18) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
((162 + -72i + -18x) + -8i * (-9 + 4i + x) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + (-9 * -8i + 4i * -8i + x * -8i) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0

Reorder the terms:
(162 + -72i + -18x + (72i + -8ix + -32i2) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + (72i + -8ix + -32i2) + -4ix * (-9 + 4i + x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + (-9 * -4ix + 4i * -4ix + x * -4ix) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0

Reorder the terms:
(162 + -72i + -18x + 72i + -8ix + -32i2 + (36ix + -4ix2 + -16i2x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + (36ix + -4ix2 + -16i2x) + -7x * (-9 + 4i + x) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-9 * -7x + 4i * -7x + x * -7x) + x2(-9 + 4i + x)) = 0

Reorder the terms:
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-28ix + 63x + -7x2) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + (-28ix + 63x + -7x2) + x2(-9 + 4i + x)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (-9 * x2 + 4i * x2 + x * x2)) = 0

Reorder the terms:
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (4ix2 + -9x2 + x3)) = 0
(162 + -72i + -18x + 72i + -8ix + -32i2 + 36ix + -4ix2 + -16i2x + -28ix + 63x + -7x2 + (4ix2 + -9x2 + x3)) = 0

Reorder the terms:
(162 + -72i + 72i + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0

Combine like terms: -72i + 72i = 0
(162 + 0 + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0
(162 + -8ix + 36ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0

Combine like terms: -8ix + 36ix = 28ix
(162 + 28ix + -28ix + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0

Combine like terms: 28ix + -28ix = 0
(162 + 0 + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0
(162 + -4ix2 + 4ix2 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0

Combine like terms: -4ix2 + 4ix2 = 0
(162 + 0 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0
(162 + -32i2 + -16i2x + -18x + 63x + -7x2 + -9x2 + x3) = 0

Combine like terms: -18x + 63x = 45x
(162 + -32i2 + -16i2x + 45x + -7x2 + -9x2 + x3) = 0

Combine like terms: -7x2 + -9x2 = -16x2
(162 + -32i2 + -16i2x + 45x + -16x2 + x3) = 0

Solving
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0

Solving for variable 'i'.

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

Add '-162' to each side of the equation.
162 + -32i2 + -16i2x + 45x + -16x2 + -162 + x3 = 0 + -162

Reorder the terms:
162 + -162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162

Combine like terms: 162 + -162 = 0
0 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162
-32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -162

Combine like terms: 0 + -162 = -162
-32i2 + -16i2x + 45x + -16x2 + x3 = -162

Add '-45x' to each side of the equation.
-32i2 + -16i2x + 45x + -16x2 + -45x + x3 = -162 + -45x

Reorder the terms:
-32i2 + -16i2x + 45x + -45x + -16x2 + x3 = -162 + -45x

Combine like terms: 45x + -45x = 0
-32i2 + -16i2x + 0 + -16x2 + x3 = -162 + -45x
-32i2 + -16i2x + -16x2 + x3 = -162 + -45x

Add '16x2' to each side of the equation.
-32i2 + -16i2x + -16x2 + 16x2 + x3 = -162 + -45x + 16x2

Combine like terms: -16x2 + 16x2 = 0
-32i2 + -16i2x + 0 + x3 = -162 + -45x + 16x2
-32i2 + -16i2x + x3 = -162 + -45x + 16x2

Add '-1x3' to each side of the equation.
-32i2 + -16i2x + x3 + -1x3 = -162 + -45x + 16x2 + -1x3

Combine like terms: x3 + -1x3 = 0
-32i2 + -16i2x + 0 = -162 + -45x + 16x2 + -1x3
-32i2 + -16i2x = -162 + -45x + 16x2 + -1x3

Reorder the terms:
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -162 + -45x + 16x2 + -1x3 + 162 + 45x + -16x2 + x3

Reorder the terms:
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -162 + 162 + -45x + 45x + 16x2 + -16x2 + -1x3 + x3

Combine like terms: -162 + 162 = 0
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -45x + 45x + 16x2 + -16x2 + -1x3 + x3
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -45x + 45x + 16x2 + -16x2 + -1x3 + x3

Combine like terms: -45x + 45x = 0
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + 16x2 + -16x2 + -1x3 + x3
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 16x2 + -16x2 + -1x3 + x3

Combine like terms: 16x2 + -16x2 = 0
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0 + -1x3 + x3
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = -1x3 + x3

Combine like terms: -1x3 + x3 = 0
162 + -32i2 + -16i2x + 45x + -16x2 + x3 = 0

The solution to this equation could not be determined.

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