Y=200+(0.8*(Y-T))+200+0.1Y+100+100-100-0.15Y

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Solution for Y=200+(0.8*(Y-T))+200+0.1Y+100+100-100-0.15Y equation: 


Simplifying
Y = 200 + (0.8(Y + -1T)) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y

Reorder the terms:
Y = 200 + (0.8(-1T + Y)) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y
Y = 200 + ((-1T * 0.8 + Y * 0.8)) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y
Y = 200 + ((-0.8T + 0.8Y)) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y
Y = 200 + (-0.8T + 0.8Y) + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y

Remove parenthesis around (-0.8T + 0.8Y)
Y = 200 + -0.8T + 0.8Y + 200 + 0.1Y + 100 + 100 + -100 + -0.15Y

Reorder the terms:
Y = 200 + 200 + 100 + 100 + -100 + -0.8T + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 200 + 200 = 400
Y = 400 + 100 + 100 + -100 + -0.8T + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 400 + 100 = 500
Y = 500 + 100 + -100 + -0.8T + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 500 + 100 = 600
Y = 600 + -100 + -0.8T + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 600 + -100 = 500
Y = 500 + -0.8T + 0.8Y + 0.1Y + -0.15Y

Combine like terms: 0.8Y + 0.1Y = 0.9Y
Y = 500 + -0.8T + 0.9Y + -0.15Y

Combine like terms: 0.9Y + -0.15Y = 0.75Y
Y = 500 + -0.8T + 0.75Y

Solving
Y = 500 + -0.8T + 0.75Y

Solving for variable 'Y'.

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

Add '-0.75Y' to each side of the equation.
Y + -0.75Y = 500 + -0.8T + 0.75Y + -0.75Y

Combine like terms: Y + -0.75Y = 0.25Y
0.25Y = 500 + -0.8T + 0.75Y + -0.75Y

Combine like terms: 0.75Y + -0.75Y = 0.00
0.25Y = 500 + -0.8T + 0.00
0.25Y = 500 + -0.8T

Divide each side by '0.25'.
Y = 2000 + -3.2T

Simplifying
Y = 2000 + -3.2T

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