(x-(4-5i))(x-(4+5i))=0

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Solution for (x-(4-5i))(x-(4+5i))=0 equation: 


Simplifying
(x + -1(4 + -5i))(x + -1(4 + 5i)) = 0
(x + (4 * -1 + -5i * -1))(x + -1(4 + 5i)) = 0
(x + (-4 + 5i))(x + -1(4 + 5i)) = 0

Reorder the terms:
(-4 + 5i + x)(x + -1(4 + 5i)) = 0
(-4 + 5i + x)(x + (4 * -1 + 5i * -1)) = 0
(-4 + 5i + x)(x + (-4 + -5i)) = 0

Reorder the terms:
(-4 + 5i + x)(-4 + -5i + x) = 0

Multiply (-4 + 5i + x) * (-4 + -5i + x)
(-4(-4 + -5i + x) + 5i * (-4 + -5i + x) + x(-4 + -5i + x)) = 0
((-4 * -4 + -5i * -4 + x * -4) + 5i * (-4 + -5i + x) + x(-4 + -5i + x)) = 0
((16 + 20i + -4x) + 5i * (-4 + -5i + x) + x(-4 + -5i + x)) = 0
(16 + 20i + -4x + (-4 * 5i + -5i * 5i + x * 5i) + x(-4 + -5i + x)) = 0

Reorder the terms:
(16 + 20i + -4x + (-20i + 5ix + -25i2) + x(-4 + -5i + x)) = 0
(16 + 20i + -4x + (-20i + 5ix + -25i2) + x(-4 + -5i + x)) = 0
(16 + 20i + -4x + -20i + 5ix + -25i2 + (-4 * x + -5i * x + x * x)) = 0

Reorder the terms:
(16 + 20i + -4x + -20i + 5ix + -25i2 + (-5ix + -4x + x2)) = 0
(16 + 20i + -4x + -20i + 5ix + -25i2 + (-5ix + -4x + x2)) = 0

Reorder the terms:
(16 + 20i + -20i + 5ix + -5ix + -25i2 + -4x + -4x + x2) = 0

Combine like terms: 20i + -20i = 0
(16 + 0 + 5ix + -5ix + -25i2 + -4x + -4x + x2) = 0
(16 + 5ix + -5ix + -25i2 + -4x + -4x + x2) = 0

Combine like terms: 5ix + -5ix = 0
(16 + 0 + -25i2 + -4x + -4x + x2) = 0
(16 + -25i2 + -4x + -4x + x2) = 0

Combine like terms: -4x + -4x = -8x
(16 + -25i2 + -8x + x2) = 0

Solving
16 + -25i2 + -8x + x2 = 0

Solving for variable 'i'.

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

Add '-16' to each side of the equation.
16 + -25i2 + -8x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -25i2 + -8x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -25i2 + -8x + x2 = 0 + -16
-25i2 + -8x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-25i2 + -8x + x2 = -16

Add '8x' to each side of the equation.
-25i2 + -8x + 8x + x2 = -16 + 8x

Combine like terms: -8x + 8x = 0
-25i2 + 0 + x2 = -16 + 8x
-25i2 + x2 = -16 + 8x

Add '-1x2' to each side of the equation.
-25i2 + x2 + -1x2 = -16 + 8x + -1x2

Combine like terms: x2 + -1x2 = 0
-25i2 + 0 = -16 + 8x + -1x2
-25i2 = -16 + 8x + -1x2

Divide each side by '-25'.
i2 = 0.64 + -0.32x + 0.04x2

Simplifying
i2 = 0.64 + -0.32x + 0.04x2

Reorder the terms:
-0.64 + i2 + 0.32x + -0.04x2 = 0.64 + -0.32x + 0.04x2 + -0.64 + 0.32x + -0.04x2

Reorder the terms:
-0.64 + i2 + 0.32x + -0.04x2 = 0.64 + -0.64 + -0.32x + 0.32x + 0.04x2 + -0.04x2

Combine like terms: 0.64 + -0.64 = 0.00
-0.64 + i2 + 0.32x + -0.04x2 = 0.00 + -0.32x + 0.32x + 0.04x2 + -0.04x2
-0.64 + i2 + 0.32x + -0.04x2 = -0.32x + 0.32x + 0.04x2 + -0.04x2

Combine like terms: -0.32x + 0.32x = 0.00
-0.64 + i2 + 0.32x + -0.04x2 = 0.00 + 0.04x2 + -0.04x2
-0.64 + i2 + 0.32x + -0.04x2 = 0.04x2 + -0.04x2

Combine like terms: 0.04x2 + -0.04x2 = 0.00
-0.64 + i2 + 0.32x + -0.04x2 = 0.00

The solution to this equation could not be determined.

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