4(Y-3)-6(y+1)=4(3y+4)-2(8-6y)

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Solution for 4(Y-3)-6(y+1)=4(3y+4)-2(8-6y) equation: 


Simplifying
4(Y + -3) + -6(y + 1) = 4(3y + 4) + -2(8 + -6y)

Reorder the terms:
4(-3 + Y) + -6(y + 1) = 4(3y + 4) + -2(8 + -6y)
(-3 * 4 + Y * 4) + -6(y + 1) = 4(3y + 4) + -2(8 + -6y)
(-12 + 4Y) + -6(y + 1) = 4(3y + 4) + -2(8 + -6y)

Reorder the terms:
-12 + 4Y + -6(1 + y) = 4(3y + 4) + -2(8 + -6y)
-12 + 4Y + (1 * -6 + y * -6) = 4(3y + 4) + -2(8 + -6y)
-12 + 4Y + (-6 + -6y) = 4(3y + 4) + -2(8 + -6y)

Reorder the terms:
-12 + -6 + 4Y + -6y = 4(3y + 4) + -2(8 + -6y)

Combine like terms: -12 + -6 = -18
-18 + 4Y + -6y = 4(3y + 4) + -2(8 + -6y)

Reorder the terms:
-18 + 4Y + -6y = 4(4 + 3y) + -2(8 + -6y)
-18 + 4Y + -6y = (4 * 4 + 3y * 4) + -2(8 + -6y)
-18 + 4Y + -6y = (16 + 12y) + -2(8 + -6y)
-18 + 4Y + -6y = 16 + 12y + (8 * -2 + -6y * -2)
-18 + 4Y + -6y = 16 + 12y + (-16 + 12y)

Reorder the terms:
-18 + 4Y + -6y = 16 + -16 + 12y + 12y

Combine like terms: 16 + -16 = 0
-18 + 4Y + -6y = 0 + 12y + 12y
-18 + 4Y + -6y = 12y + 12y

Combine like terms: 12y + 12y = 24y
-18 + 4Y + -6y = 24y

Solving
-18 + 4Y + -6y = 24y

Solving for variable 'Y'.

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

Add '18' to each side of the equation.
-18 + 4Y + 18 + -6y = 18 + 24y

Reorder the terms:
-18 + 18 + 4Y + -6y = 18 + 24y

Combine like terms: -18 + 18 = 0
0 + 4Y + -6y = 18 + 24y
4Y + -6y = 18 + 24y

Add '6y' to each side of the equation.
4Y + -6y + 6y = 18 + 24y + 6y

Combine like terms: -6y + 6y = 0
4Y + 0 = 18 + 24y + 6y
4Y = 18 + 24y + 6y

Combine like terms: 24y + 6y = 30y
4Y = 18 + 30y

Divide each side by '4'.
Y = 4.5 + 7.5y

Simplifying
Y = 4.5 + 7.5y

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