Y=100+0.5*(Y-200)+200+0.1*Y-40*i+200

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Solution for Y=100+0.5*(Y-200)+200+0.1*Y-40*i+200 equation: 


Simplifying
Y = 100 + 0.5(Y + -200) + 200 + 0.1Y + -40i + 200

Reorder the terms:
Y = 100 + 0.5(-200 + Y) + 200 + 0.1Y + -40i + 200
Y = 100 + (-200 * 0.5 + Y * 0.5) + 200 + 0.1Y + -40i + 200
Y = 100 + (-100 + 0.5Y) + 200 + 0.1Y + -40i + 200

Reorder the terms:
Y = 100 + -100 + 200 + 200 + 0.5Y + 0.1Y + -40i

Combine like terms: 100 + -100 = 0
Y = 0 + 200 + 200 + 0.5Y + 0.1Y + -40i
Y = 200 + 200 + 0.5Y + 0.1Y + -40i

Combine like terms: 200 + 200 = 400
Y = 400 + 0.5Y + 0.1Y + -40i

Combine like terms: 0.5Y + 0.1Y = 0.6Y
Y = 400 + 0.6Y + -40i

Solving
Y = 400 + 0.6Y + -40i

Solving for variable 'Y'.

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

Add '-0.6Y' to each side of the equation.
Y + -0.6Y = 400 + 0.6Y + -0.6Y + -40i

Combine like terms: Y + -0.6Y = 0.4Y
0.4Y = 400 + 0.6Y + -0.6Y + -40i

Combine like terms: 0.6Y + -0.6Y = 0.0
0.4Y = 400 + 0.0 + -40i
0.4Y = 400 + -40i

Divide each side by '0.4'.
Y = 1000 + -100i

Simplifying
Y = 1000 + -100i

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