45+-.5y+3(45-.5Y)+2Y=180

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Solution for 45+-.5y+3(45-.5Y)+2Y=180 equation: 


Simplifying
45 + -0.5y + 3(45 + -0.5Y) + 2Y = 180
45 + -0.5y + (45 * 3 + -0.5Y * 3) + 2Y = 180
45 + -0.5y + (135 + -1.5Y) + 2Y = 180

Reorder the terms:
45 + 135 + -1.5Y + 2Y + -0.5y = 180

Combine like terms: 45 + 135 = 180
180 + -1.5Y + 2Y + -0.5y = 180

Combine like terms: -1.5Y + 2Y = 0.5Y
180 + 0.5Y + -0.5y = 180

Add '-180' to each side of the equation.
180 + 0.5Y + -180 + -0.5y = 180 + -180

Reorder the terms:
180 + -180 + 0.5Y + -0.5y = 180 + -180

Combine like terms: 180 + -180 = 0
0 + 0.5Y + -0.5y = 180 + -180
0.5Y + -0.5y = 180 + -180

Combine like terms: 180 + -180 = 0
0.5Y + -0.5y = 0

Solving
0.5Y + -0.5y = 0

Solving for variable 'Y'.

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

Add '0.5y' to each side of the equation.
0.5Y + -0.5y + 0.5y = 0 + 0.5y

Combine like terms: -0.5y + 0.5y = 0.0
0.5Y + 0.0 = 0 + 0.5y
0.5Y = 0 + 0.5y
Remove the zero:
0.5Y = 0.5y

Divide each side by '0.5'.
Y = y

Simplifying
Y = y

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