(x+1-4i)(x+1+4i)=0

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Solution for (x+1-4i)(x+1+4i)=0 equation: 


Simplifying
(x + 1 + -4i)(x + 1 + 4i) = 0

Reorder the terms:
(1 + -4i + x)(x + 1 + 4i) = 0

Reorder the terms:
(1 + -4i + x)(1 + 4i + x) = 0

Multiply (1 + -4i + x) * (1 + 4i + x)
(1(1 + 4i + x) + -4i * (1 + 4i + x) + x(1 + 4i + x)) = 0
((1 * 1 + 4i * 1 + x * 1) + -4i * (1 + 4i + x) + x(1 + 4i + x)) = 0
((1 + 4i + 1x) + -4i * (1 + 4i + x) + x(1 + 4i + x)) = 0
(1 + 4i + 1x + (1 * -4i + 4i * -4i + x * -4i) + x(1 + 4i + x)) = 0

Reorder the terms:
(1 + 4i + 1x + (-4i + -4ix + -16i2) + x(1 + 4i + x)) = 0
(1 + 4i + 1x + (-4i + -4ix + -16i2) + x(1 + 4i + x)) = 0
(1 + 4i + 1x + -4i + -4ix + -16i2 + (1 * x + 4i * x + x * x)) = 0

Reorder the terms:
(1 + 4i + 1x + -4i + -4ix + -16i2 + (4ix + 1x + x2)) = 0
(1 + 4i + 1x + -4i + -4ix + -16i2 + (4ix + 1x + x2)) = 0

Reorder the terms:
(1 + 4i + -4i + -4ix + 4ix + -16i2 + 1x + 1x + x2) = 0

Combine like terms: 4i + -4i = 0
(1 + 0 + -4ix + 4ix + -16i2 + 1x + 1x + x2) = 0
(1 + -4ix + 4ix + -16i2 + 1x + 1x + x2) = 0

Combine like terms: -4ix + 4ix = 0
(1 + 0 + -16i2 + 1x + 1x + x2) = 0
(1 + -16i2 + 1x + 1x + x2) = 0

Combine like terms: 1x + 1x = 2x
(1 + -16i2 + 2x + x2) = 0

Solving
1 + -16i2 + 2x + x2 = 0

Solving for variable 'i'.

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

Add '-1' to each side of the equation.
1 + -16i2 + 2x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -16i2 + 2x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -16i2 + 2x + x2 = 0 + -1
-16i2 + 2x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-16i2 + 2x + x2 = -1

Add '-2x' to each side of the equation.
-16i2 + 2x + -2x + x2 = -1 + -2x

Combine like terms: 2x + -2x = 0
-16i2 + 0 + x2 = -1 + -2x
-16i2 + x2 = -1 + -2x

Add '-1x2' to each side of the equation.
-16i2 + x2 + -1x2 = -1 + -2x + -1x2

Combine like terms: x2 + -1x2 = 0
-16i2 + 0 = -1 + -2x + -1x2
-16i2 = -1 + -2x + -1x2

Divide each side by '-16'.
i2 = 0.0625 + 0.125x + 0.0625x2

Simplifying
i2 = 0.0625 + 0.125x + 0.0625x2

Reorder the terms:
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.0625 + 0.125x + 0.0625x2 + -0.0625 + -0.125x + -0.0625x2

Reorder the terms:
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.0625 + -0.0625 + 0.125x + -0.125x + 0.0625x2 + -0.0625x2

Combine like terms: 0.0625 + -0.0625 = 0.0000
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.0000 + 0.125x + -0.125x + 0.0625x2 + -0.0625x2
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.125x + -0.125x + 0.0625x2 + -0.0625x2

Combine like terms: 0.125x + -0.125x = 0.000
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.000 + 0.0625x2 + -0.0625x2
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.0625x2 + -0.0625x2

Combine like terms: 0.0625x2 + -0.0625x2 = 0.0000
-0.0625 + i2 + -0.125x + -0.0625x2 = 0.0000

The solution to this equation could not be determined.

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