55-(3+5y-2(y+2))=-3(5y-5)-(5(y-1)-12y+4)

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Solution for 55-(3+5y-2(y+2))=-3(5y-5)-(5(y-1)-12y+4) equation: 


Simplifying
55 + -1(3 + 5y + -2(y + 2)) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Reorder the terms:
55 + -1(3 + 5y + -2(2 + y)) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)
55 + -1(3 + 5y + (2 * -2 + y * -2)) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)
55 + -1(3 + 5y + (-4 + -2y)) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Reorder the terms:
55 + -1(3 + -4 + 5y + -2y) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Combine like terms: 3 + -4 = -1
55 + -1(-1 + 5y + -2y) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Combine like terms: 5y + -2y = 3y
55 + -1(-1 + 3y) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)
55 + (-1 * -1 + 3y * -1) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)
55 + (1 + -3y) = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Combine like terms: 55 + 1 = 56
56 + -3y = -3(5y + -5) + -1(5(y + -1) + -12y + 4)

Reorder the terms:
56 + -3y = -3(-5 + 5y) + -1(5(y + -1) + -12y + 4)
56 + -3y = (-5 * -3 + 5y * -3) + -1(5(y + -1) + -12y + 4)
56 + -3y = (15 + -15y) + -1(5(y + -1) + -12y + 4)

Reorder the terms:
56 + -3y = 15 + -15y + -1(5(-1 + y) + -12y + 4)
56 + -3y = 15 + -15y + -1((-1 * 5 + y * 5) + -12y + 4)
56 + -3y = 15 + -15y + -1((-5 + 5y) + -12y + 4)

Reorder the terms:
56 + -3y = 15 + -15y + -1(-5 + 4 + 5y + -12y)

Combine like terms: -5 + 4 = -1
56 + -3y = 15 + -15y + -1(-1 + 5y + -12y)

Combine like terms: 5y + -12y = -7y
56 + -3y = 15 + -15y + -1(-1 + -7y)
56 + -3y = 15 + -15y + (-1 * -1 + -7y * -1)
56 + -3y = 15 + -15y + (1 + 7y)

Reorder the terms:
56 + -3y = 15 + 1 + -15y + 7y

Combine like terms: 15 + 1 = 16
56 + -3y = 16 + -15y + 7y

Combine like terms: -15y + 7y = -8y
56 + -3y = 16 + -8y

Solving
56 + -3y = 16 + -8y

Solving for variable 'y'.

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

Add '8y' to each side of the equation.
56 + -3y + 8y = 16 + -8y + 8y

Combine like terms: -3y + 8y = 5y
56 + 5y = 16 + -8y + 8y

Combine like terms: -8y + 8y = 0
56 + 5y = 16 + 0
56 + 5y = 16

Add '-56' to each side of the equation.
56 + -56 + 5y = 16 + -56

Combine like terms: 56 + -56 = 0
0 + 5y = 16 + -56
5y = 16 + -56

Combine like terms: 16 + -56 = -40
5y = -40

Divide each side by '5'.
y = -8

Simplifying
y = -8

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