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

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


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

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

Multiply (5 + x) * (4 + -1i)
(5(4 + -1i) + x(4 + -1i))(4 + i) = 0
((4 * 5 + -1i * 5) + x(4 + -1i))(4 + i) = 0
((20 + -5i) + x(4 + -1i))(4 + i) = 0
(20 + -5i + (4 * x + -1i * x))(4 + i) = 0

Reorder the terms:
(20 + -5i + (-1ix + 4x))(4 + i) = 0
(20 + -5i + (-1ix + 4x))(4 + i) = 0
(20 + -5i + -1ix + 4x)(4 + i) = 0

Multiply (20 + -5i + -1ix + 4x) * (4 + i)
(20(4 + i) + -5i * (4 + i) + -1ix * (4 + i) + 4x * (4 + i)) = 0
((4 * 20 + i * 20) + -5i * (4 + i) + -1ix * (4 + i) + 4x * (4 + i)) = 0
((80 + 20i) + -5i * (4 + i) + -1ix * (4 + i) + 4x * (4 + i)) = 0
(80 + 20i + (4 * -5i + i * -5i) + -1ix * (4 + i) + 4x * (4 + i)) = 0
(80 + 20i + (-20i + -5i2) + -1ix * (4 + i) + 4x * (4 + i)) = 0
(80 + 20i + -20i + -5i2 + (4 * -1ix + i * -1ix) + 4x * (4 + i)) = 0
(80 + 20i + -20i + -5i2 + (-4ix + -1i2x) + 4x * (4 + i)) = 0
(80 + 20i + -20i + -5i2 + -4ix + -1i2x + (4 * 4x + i * 4x)) = 0

Reorder the terms:
(80 + 20i + -20i + -5i2 + -4ix + -1i2x + (4ix + 16x)) = 0
(80 + 20i + -20i + -5i2 + -4ix + -1i2x + (4ix + 16x)) = 0

Reorder the terms:
(80 + 20i + -20i + -4ix + 4ix + -5i2 + -1i2x + 16x) = 0

Combine like terms: 20i + -20i = 0
(80 + 0 + -4ix + 4ix + -5i2 + -1i2x + 16x) = 0
(80 + -4ix + 4ix + -5i2 + -1i2x + 16x) = 0

Combine like terms: -4ix + 4ix = 0
(80 + 0 + -5i2 + -1i2x + 16x) = 0
(80 + -5i2 + -1i2x + 16x) = 0

Solving
80 + -5i2 + -1i2x + 16x = 0

Solving for variable 'i'.

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

Add '-80' to each side of the equation.
80 + -5i2 + -1i2x + -80 + 16x = 0 + -80

Reorder the terms:
80 + -80 + -5i2 + -1i2x + 16x = 0 + -80

Combine like terms: 80 + -80 = 0
0 + -5i2 + -1i2x + 16x = 0 + -80
-5i2 + -1i2x + 16x = 0 + -80

Combine like terms: 0 + -80 = -80
-5i2 + -1i2x + 16x = -80

Add '-16x' to each side of the equation.
-5i2 + -1i2x + 16x + -16x = -80 + -16x

Combine like terms: 16x + -16x = 0
-5i2 + -1i2x + 0 = -80 + -16x
-5i2 + -1i2x = -80 + -16x

Reorder the terms:
80 + -5i2 + -1i2x + 16x = -80 + -16x + 80 + 16x

Reorder the terms:
80 + -5i2 + -1i2x + 16x = -80 + 80 + -16x + 16x

Combine like terms: -80 + 80 = 0
80 + -5i2 + -1i2x + 16x = 0 + -16x + 16x
80 + -5i2 + -1i2x + 16x = -16x + 16x

Combine like terms: -16x + 16x = 0
80 + -5i2 + -1i2x + 16x = 0

The solution to this equation could not be determined.

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