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

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


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

Reorder the terms:
Y = (100 + 0.8(-100 + Y)) + 200 + 100
Y = (100 + (-100 * 0.8 + Y * 0.8)) + 200 + 100
Y = (100 + (-80 + 0.8Y)) + 200 + 100

Combine like terms: 100 + -80 = 20
Y = (20 + 0.8Y) + 200 + 100

Remove parenthesis around (20 + 0.8Y)
Y = 20 + 0.8Y + 200 + 100

Reorder the terms:
Y = 20 + 200 + 100 + 0.8Y

Combine like terms: 20 + 200 = 220
Y = 220 + 100 + 0.8Y

Combine like terms: 220 + 100 = 320
Y = 320 + 0.8Y

Solving
Y = 320 + 0.8Y

Solving for variable 'Y'.

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

Add '-0.8Y' to each side of the equation.
Y + -0.8Y = 320 + 0.8Y + -0.8Y

Combine like terms: Y + -0.8Y = 0.2Y
0.2Y = 320 + 0.8Y + -0.8Y

Combine like terms: 0.8Y + -0.8Y = 0.0
0.2Y = 320 + 0.0
0.2Y = 320

Divide each side by '0.2'.
Y = 1600

Simplifying
Y = 1600

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