(x+(8-3i))(x+(8+3i))=0

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Solution for (x+(8-3i))(x+(8+3i))=0 equation:


Simplifying
(x + (8 + -3i))(x + (8 + 3i)) = 0

Remove parenthesis around (8 + -3i)
(x + 8 + -3i)(x + (8 + 3i)) = 0

Reorder the terms:
(8 + -3i + x)(x + (8 + 3i)) = 0

Remove parenthesis around (8 + 3i)
(8 + -3i + x)(x + 8 + 3i) = 0

Reorder the terms:
(8 + -3i + x)(8 + 3i + x) = 0

Multiply (8 + -3i + x) * (8 + 3i + x)
(8(8 + 3i + x) + -3i * (8 + 3i + x) + x(8 + 3i + x)) = 0
((8 * 8 + 3i * 8 + x * 8) + -3i * (8 + 3i + x) + x(8 + 3i + x)) = 0
((64 + 24i + 8x) + -3i * (8 + 3i + x) + x(8 + 3i + x)) = 0
(64 + 24i + 8x + (8 * -3i + 3i * -3i + x * -3i) + x(8 + 3i + x)) = 0

Reorder the terms:
(64 + 24i + 8x + (-24i + -3ix + -9i2) + x(8 + 3i + x)) = 0
(64 + 24i + 8x + (-24i + -3ix + -9i2) + x(8 + 3i + x)) = 0
(64 + 24i + 8x + -24i + -3ix + -9i2 + (8 * x + 3i * x + x * x)) = 0

Reorder the terms:
(64 + 24i + 8x + -24i + -3ix + -9i2 + (3ix + 8x + x2)) = 0
(64 + 24i + 8x + -24i + -3ix + -9i2 + (3ix + 8x + x2)) = 0

Reorder the terms:
(64 + 24i + -24i + -3ix + 3ix + -9i2 + 8x + 8x + x2) = 0

Combine like terms: 24i + -24i = 0
(64 + 0 + -3ix + 3ix + -9i2 + 8x + 8x + x2) = 0
(64 + -3ix + 3ix + -9i2 + 8x + 8x + x2) = 0

Combine like terms: -3ix + 3ix = 0
(64 + 0 + -9i2 + 8x + 8x + x2) = 0
(64 + -9i2 + 8x + 8x + x2) = 0

Combine like terms: 8x + 8x = 16x
(64 + -9i2 + 16x + x2) = 0

Solving
64 + -9i2 + 16x + x2 = 0

Solving for variable 'i'.

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

Add '-64' to each side of the equation.
64 + -9i2 + 16x + -64 + x2 = 0 + -64

Reorder the terms:
64 + -64 + -9i2 + 16x + x2 = 0 + -64

Combine like terms: 64 + -64 = 0
0 + -9i2 + 16x + x2 = 0 + -64
-9i2 + 16x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-9i2 + 16x + x2 = -64

Add '-16x' to each side of the equation.
-9i2 + 16x + -16x + x2 = -64 + -16x

Combine like terms: 16x + -16x = 0
-9i2 + 0 + x2 = -64 + -16x
-9i2 + x2 = -64 + -16x

Add '-1x2' to each side of the equation.
-9i2 + x2 + -1x2 = -64 + -16x + -1x2

Combine like terms: x2 + -1x2 = 0
-9i2 + 0 = -64 + -16x + -1x2
-9i2 = -64 + -16x + -1x2

Divide each side by '-9'.
i2 = 7.111111111 + 1.777777778x + 0.1111111111x2

Simplifying
i2 = 7.111111111 + 1.777777778x + 0.1111111111x2

Reorder the terms:
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 7.111111111 + 1.777777778x + 0.1111111111x2 + -7.111111111 + -1.777777778x + -0.1111111111x2

Reorder the terms:
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 7.111111111 + -7.111111111 + 1.777777778x + -1.777777778x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: 7.111111111 + -7.111111111 = 0.000000000
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 0.000000000 + 1.777777778x + -1.777777778x + 0.1111111111x2 + -0.1111111111x2
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 1.777777778x + -1.777777778x + 0.1111111111x2 + -0.1111111111x2

Combine like terms: 1.777777778x + -1.777777778x = 0.000000000
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 0.000000000 + 0.1111111111x2 + -0.1111111111x2
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 0.1111111111x2 + -0.1111111111x2

Combine like terms: 0.1111111111x2 + -0.1111111111x2 = 0.0000000000
-7.111111111 + i2 + -1.777777778x + -0.1111111111x2 = 0.0000000000

The solution to this equation could not be determined.

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