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

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


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

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

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

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

Combine like terms: 100 + 200 = 300
i = 300 + 200 + 0.5Y + 0.1Y + -40i

Combine like terms: 300 + 200 = 500
i = 500 + 0.5Y + 0.1Y + -40i

Combine like terms: 0.5Y + 0.1Y = 0.6Y
i = 500 + 0.6Y + -40i

Solving
i = 500 + 0.6Y + -40i

Solving for variable 'i'.

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

Add '40i' to each side of the equation.
i + 40i = 500 + 0.6Y + -40i + 40i

Combine like terms: i + 40i = 41i
41i = 500 + 0.6Y + -40i + 40i

Combine like terms: -40i + 40i = 0
41i = 500 + 0.6Y + 0
41i = 500 + 0.6Y

Divide each side by '41'.
i = 12.19512195 + 0.01463414634Y

Simplifying
i = 12.19512195 + 0.01463414634Y

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