What is the answer to (x-(-5-8.66i))/1+x/(6i)+x/((2-2i))=0 ?

The answer to (x-(-5-8.66i))/1+x/(6i)+x/((2-2i))=0 is x=-4.44212…-6.63185…i

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(x-(-5-8.66i))/1+x/(6i)+x/((2-2i))=0

\frac{x - ( - 5 - 8.66 i )}{1} + \frac{x}{6 i} + \frac{x}{( 2 - 2 i )} = 0

x = - 4.44212 \dots - 6.63185 \dots i

Solution steps

\frac{x - ( - 5 - 8.66 i )}{1} + \frac{x}{6 i} + \frac{x}{( 2 - 2 i )} = 0

Apply rule

\frac{a}{1} = a

x - (- 5 - 8.66 i) + \frac{x}{6 i} + \frac{x}{2 - 2 i} = 0

Multiply by LCM

x \cdot 6 i (2 - 2 i) - (- 5 - 8.66 i) \cdot 6 i (2 - 2 i) + (2 - 2 i) x + 6 i x = 0

Expand

x \cdot 6 i (2 - 2 i) - (- 5 - 8.66 i) \cdot 6 i (2 - 2 i) + (2 - 2 i) x + 6 i x : 16 i x + 14 x + 163.92 i - 43.92

16 i x + 14 x + 163.92 i - 43.92 = 0

Move

163.92 i

to the right side

16 i x + 14 x - 43.92 = - 163.92 i

Move

43.92

to the right side

16 i x + 14 x = - 163.92 i + 43.92

Factor

16 i x + 14 x : 2 (8 i + 7) x

2 (8 i + 7) x = - 163.92 i + 43.92

Divide both sides by

2 (8 i + 7)

x = - 4.44212 \dots - 6.63185 \dots i

x^{2} - 3 x - 28

5 e^{0}

\frac{π}{6} + 2 π

4 x^{2} - 16 x = 0

p^{2} - 4 p - 21 = 0

What is the answer to (x-(-5-8.66i))/1+x/(6i)+x/((2-2i))=0 ?
The answer to (x-(-5-8.66i))/1+x/(6i)+x/((2-2i))=0 is x=-4.44212…-6.63185…i