(x+6)(x+3)(x+7)(x+5i)=0

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Solution for (x+6)(x+3)(x+7)(x+5i)=0 equation: 


Simplifying
(x + 6)(x + 3)(x + 7)(x + 5i) = 0

Reorder the terms:
(6 + x)(x + 3)(x + 7)(x + 5i) = 0

Reorder the terms:
(6 + x)(3 + x)(x + 7)(x + 5i) = 0

Reorder the terms:
(6 + x)(3 + x)(7 + x)(x + 5i) = 0

Reorder the terms:
(6 + x)(3 + x)(7 + x)(5i + x) = 0

Multiply (6 + x) * (3 + x)
(6(3 + x) + x(3 + x))(7 + x)(5i + x) = 0
((3 * 6 + x * 6) + x(3 + x))(7 + x)(5i + x) = 0
((18 + 6x) + x(3 + x))(7 + x)(5i + x) = 0
(18 + 6x + (3 * x + x * x))(7 + x)(5i + x) = 0
(18 + 6x + (3x + x2))(7 + x)(5i + x) = 0

Combine like terms: 6x + 3x = 9x
(18 + 9x + x2)(7 + x)(5i + x) = 0

Multiply (18 + 9x + x2) * (7 + x)
(18(7 + x) + 9x * (7 + x) + x2(7 + x))(5i + x) = 0
((7 * 18 + x * 18) + 9x * (7 + x) + x2(7 + x))(5i + x) = 0
((126 + 18x) + 9x * (7 + x) + x2(7 + x))(5i + x) = 0
(126 + 18x + (7 * 9x + x * 9x) + x2(7 + x))(5i + x) = 0
(126 + 18x + (63x + 9x2) + x2(7 + x))(5i + x) = 0
(126 + 18x + 63x + 9x2 + (7 * x2 + x * x2))(5i + x) = 0
(126 + 18x + 63x + 9x2 + (7x2 + x3))(5i + x) = 0

Combine like terms: 18x + 63x = 81x
(126 + 81x + 9x2 + 7x2 + x3)(5i + x) = 0

Combine like terms: 9x2 + 7x2 = 16x2
(126 + 81x + 16x2 + x3)(5i + x) = 0

Multiply (126 + 81x + 16x2 + x3) * (5i + x)
(126(5i + x) + 81x * (5i + x) + 16x2 * (5i + x) + x3(5i + x)) = 0
((5i * 126 + x * 126) + 81x * (5i + x) + 16x2 * (5i + x) + x3(5i + x)) = 0
((630i + 126x) + 81x * (5i + x) + 16x2 * (5i + x) + x3(5i + x)) = 0
(630i + 126x + (5i * 81x + x * 81x) + 16x2 * (5i + x) + x3(5i + x)) = 0
(630i + 126x + (405ix + 81x2) + 16x2 * (5i + x) + x3(5i + x)) = 0
(630i + 126x + 405ix + 81x2 + (5i * 16x2 + x * 16x2) + x3(5i + x)) = 0
(630i + 126x + 405ix + 81x2 + (80ix2 + 16x3) + x3(5i + x)) = 0
(630i + 126x + 405ix + 81x2 + 80ix2 + 16x3 + (5i * x3 + x * x3)) = 0
(630i + 126x + 405ix + 81x2 + 80ix2 + 16x3 + (5ix3 + x4)) = 0

Reorder the terms:
(630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4) = 0
(630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4) = 0

Solving
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = 0

Solving for variable 'i'.

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

Add '-126x' to each side of the equation.
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + -126x + x4 = 0 + -126x

Reorder the terms:
630i + 405ix + 80ix2 + 5ix3 + 126x + -126x + 81x2 + 16x3 + x4 = 0 + -126x

Combine like terms: 126x + -126x = 0
630i + 405ix + 80ix2 + 5ix3 + 0 + 81x2 + 16x3 + x4 = 0 + -126x
630i + 405ix + 80ix2 + 5ix3 + 81x2 + 16x3 + x4 = 0 + -126x
Remove the zero:
630i + 405ix + 80ix2 + 5ix3 + 81x2 + 16x3 + x4 = -126x

Add '-81x2' to each side of the equation.
630i + 405ix + 80ix2 + 5ix3 + 81x2 + 16x3 + -81x2 + x4 = -126x + -81x2

Reorder the terms:
630i + 405ix + 80ix2 + 5ix3 + 81x2 + -81x2 + 16x3 + x4 = -126x + -81x2

Combine like terms: 81x2 + -81x2 = 0
630i + 405ix + 80ix2 + 5ix3 + 0 + 16x3 + x4 = -126x + -81x2
630i + 405ix + 80ix2 + 5ix3 + 16x3 + x4 = -126x + -81x2

Add '-16x3' to each side of the equation.
630i + 405ix + 80ix2 + 5ix3 + 16x3 + -16x3 + x4 = -126x + -81x2 + -16x3

Combine like terms: 16x3 + -16x3 = 0
630i + 405ix + 80ix2 + 5ix3 + 0 + x4 = -126x + -81x2 + -16x3
630i + 405ix + 80ix2 + 5ix3 + x4 = -126x + -81x2 + -16x3

Add '-1x4' to each side of the equation.
630i + 405ix + 80ix2 + 5ix3 + x4 + -1x4 = -126x + -81x2 + -16x3 + -1x4

Combine like terms: x4 + -1x4 = 0
630i + 405ix + 80ix2 + 5ix3 + 0 = -126x + -81x2 + -16x3 + -1x4
630i + 405ix + 80ix2 + 5ix3 = -126x + -81x2 + -16x3 + -1x4

Reorder the terms:
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = -126x + 126x + -81x2 + 81x2 + -16x3 + 16x3 + -1x4 + x4

Combine like terms: -126x + 126x = 0
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = 0 + -81x2 + 81x2 + -16x3 + 16x3 + -1x4 + x4
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = -81x2 + 81x2 + -16x3 + 16x3 + -1x4 + x4

Combine like terms: -81x2 + 81x2 = 0
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = 0 + -16x3 + 16x3 + -1x4 + x4
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = -16x3 + 16x3 + -1x4 + x4

Combine like terms: -16x3 + 16x3 = 0
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = 0 + -1x4 + x4
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = -1x4 + x4

Combine like terms: -1x4 + x4 = 0
630i + 405ix + 80ix2 + 5ix3 + 126x + 81x2 + 16x3 + x4 = 0

The solution to this equation could not be determined.

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