16-[4+5y-2(y+5)]=-3(4y-3)-[5(y-1)-12y+2]

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Solution for 16-[4+5y-2(y+5)]=-3(4y-3)-[5(y-1)-12y+2] equation: 


Simplifying
16 + -1[4 + 5y + -2(y + 5)] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Reorder the terms:
16 + -1[4 + 5y + -2(5 + y)] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]
16 + -1[4 + 5y + (5 * -2 + y * -2)] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]
16 + -1[4 + 5y + (-10 + -2y)] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Reorder the terms:
16 + -1[4 + -10 + 5y + -2y] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Combine like terms: 4 + -10 = -6
16 + -1[-6 + 5y + -2y] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Combine like terms: 5y + -2y = 3y
16 + -1[-6 + 3y] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]
16 + [-6 * -1 + 3y * -1] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]
16 + [6 + -3y] = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Combine like terms: 16 + 6 = 22
22 + -3y = -3(4y + -3) + -1[5(y + -1) + -12y + 2]

Reorder the terms:
22 + -3y = -3(-3 + 4y) + -1[5(y + -1) + -12y + 2]
22 + -3y = (-3 * -3 + 4y * -3) + -1[5(y + -1) + -12y + 2]
22 + -3y = (9 + -12y) + -1[5(y + -1) + -12y + 2]

Reorder the terms:
22 + -3y = 9 + -12y + -1[5(-1 + y) + -12y + 2]
22 + -3y = 9 + -12y + -1[(-1 * 5 + y * 5) + -12y + 2]
22 + -3y = 9 + -12y + -1[(-5 + 5y) + -12y + 2]

Reorder the terms:
22 + -3y = 9 + -12y + -1[-5 + 2 + 5y + -12y]

Combine like terms: -5 + 2 = -3
22 + -3y = 9 + -12y + -1[-3 + 5y + -12y]

Combine like terms: 5y + -12y = -7y
22 + -3y = 9 + -12y + -1[-3 + -7y]
22 + -3y = 9 + -12y + [-3 * -1 + -7y * -1]
22 + -3y = 9 + -12y + [3 + 7y]

Reorder the terms:
22 + -3y = 9 + 3 + -12y + 7y

Combine like terms: 9 + 3 = 12
22 + -3y = 12 + -12y + 7y

Combine like terms: -12y + 7y = -5y
22 + -3y = 12 + -5y

Solving
22 + -3y = 12 + -5y

Solving for variable 'y'.

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

Add '5y' to each side of the equation.
22 + -3y + 5y = 12 + -5y + 5y

Combine like terms: -3y + 5y = 2y
22 + 2y = 12 + -5y + 5y

Combine like terms: -5y + 5y = 0
22 + 2y = 12 + 0
22 + 2y = 12

Add '-22' to each side of the equation.
22 + -22 + 2y = 12 + -22

Combine like terms: 22 + -22 = 0
0 + 2y = 12 + -22
2y = 12 + -22

Combine like terms: 12 + -22 = -10
2y = -10

Divide each side by '2'.
y = -5

Simplifying
y = -5

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