6(Y-4)-4(5y+1)=3(y-2)-4(2y+1)

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Solution for 6(Y-4)-4(5y+1)=3(y-2)-4(2y+1) equation: 


Simplifying
6(Y + -4) + -4(5y + 1) = 3(y + -2) + -4(2y + 1)

Reorder the terms:
6(-4 + Y) + -4(5y + 1) = 3(y + -2) + -4(2y + 1)
(-4 * 6 + Y * 6) + -4(5y + 1) = 3(y + -2) + -4(2y + 1)
(-24 + 6Y) + -4(5y + 1) = 3(y + -2) + -4(2y + 1)

Reorder the terms:
-24 + 6Y + -4(1 + 5y) = 3(y + -2) + -4(2y + 1)
-24 + 6Y + (1 * -4 + 5y * -4) = 3(y + -2) + -4(2y + 1)
-24 + 6Y + (-4 + -20y) = 3(y + -2) + -4(2y + 1)

Reorder the terms:
-24 + -4 + 6Y + -20y = 3(y + -2) + -4(2y + 1)

Combine like terms: -24 + -4 = -28
-28 + 6Y + -20y = 3(y + -2) + -4(2y + 1)

Reorder the terms:
-28 + 6Y + -20y = 3(-2 + y) + -4(2y + 1)
-28 + 6Y + -20y = (-2 * 3 + y * 3) + -4(2y + 1)
-28 + 6Y + -20y = (-6 + 3y) + -4(2y + 1)

Reorder the terms:
-28 + 6Y + -20y = -6 + 3y + -4(1 + 2y)
-28 + 6Y + -20y = -6 + 3y + (1 * -4 + 2y * -4)
-28 + 6Y + -20y = -6 + 3y + (-4 + -8y)

Reorder the terms:
-28 + 6Y + -20y = -6 + -4 + 3y + -8y

Combine like terms: -6 + -4 = -10
-28 + 6Y + -20y = -10 + 3y + -8y

Combine like terms: 3y + -8y = -5y
-28 + 6Y + -20y = -10 + -5y

Solving
-28 + 6Y + -20y = -10 + -5y

Solving for variable 'Y'.

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

Add '28' to each side of the equation.
-28 + 6Y + 28 + -20y = -10 + 28 + -5y

Reorder the terms:
-28 + 28 + 6Y + -20y = -10 + 28 + -5y

Combine like terms: -28 + 28 = 0
0 + 6Y + -20y = -10 + 28 + -5y
6Y + -20y = -10 + 28 + -5y

Combine like terms: -10 + 28 = 18
6Y + -20y = 18 + -5y

Add '20y' to each side of the equation.
6Y + -20y + 20y = 18 + -5y + 20y

Combine like terms: -20y + 20y = 0
6Y + 0 = 18 + -5y + 20y
6Y = 18 + -5y + 20y

Combine like terms: -5y + 20y = 15y
6Y = 18 + 15y

Divide each side by '6'.
Y = 3 + 2.5y

Simplifying
Y = 3 + 2.5y

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