Y=200+0.8(Y-200)+200+0.1(Y)+100+100-100.15(Y)

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Solution for Y=200+0.8(Y-200)+200+0.1(Y)+100+100-100.15(Y) equation: 


Simplifying
Y = 200 + 0.8(Y + -200) + 200 + 0.1(Y) + 100 + 100 + -100.15(Y)

Reorder the terms:
Y = 200 + 0.8(-200 + Y) + 200 + 0.1(Y) + 100 + 100 + -100.15(Y)
Y = 200 + (-200 * 0.8 + Y * 0.8) + 200 + 0.1(Y) + 100 + 100 + -100.15(Y)
Y = 200 + (-160 + 0.8Y) + 200 + 0.1(Y) + 100 + 100 + -100.15(Y)

Reorder the terms:
Y = 200 + -160 + 200 + 100 + 100 + 0.8Y + 0.1Y + -100.15Y

Combine like terms: 200 + -160 = 40
Y = 40 + 200 + 100 + 100 + 0.8Y + 0.1Y + -100.15Y

Combine like terms: 40 + 200 = 240
Y = 240 + 100 + 100 + 0.8Y + 0.1Y + -100.15Y

Combine like terms: 240 + 100 = 340
Y = 340 + 100 + 0.8Y + 0.1Y + -100.15Y

Combine like terms: 340 + 100 = 440
Y = 440 + 0.8Y + 0.1Y + -100.15Y

Combine like terms: 0.8Y + 0.1Y = 0.9Y
Y = 440 + 0.9Y + -100.15Y

Combine like terms: 0.9Y + -100.15Y = -99.25Y
Y = 440 + -99.25Y

Solving
Y = 440 + -99.25Y

Solving for variable 'Y'.

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

Add '99.25Y' to each side of the equation.
Y + 99.25Y = 440 + -99.25Y + 99.25Y

Combine like terms: Y + 99.25Y = 100.25Y
100.25Y = 440 + -99.25Y + 99.25Y

Combine like terms: -99.25Y + 99.25Y = 0.00
100.25Y = 440 + 0.00
100.25Y = 440

Divide each side by '100.25'.
Y = 4.389027431

Simplifying
Y = 4.389027431

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