42-[4+8y-3(y+4)]=-2(4y-5)-[7(y-1)-1y+3]

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Solution for 42-[4+8y-3(y+4)]=-2(4y-5)-[7(y-1)-1y+3] equation: 


Simplifying
42 + -1[4 + 8y + -3(y + 4)] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Reorder the terms:
42 + -1[4 + 8y + -3(4 + y)] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]
42 + -1[4 + 8y + (4 * -3 + y * -3)] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]
42 + -1[4 + 8y + (-12 + -3y)] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Reorder the terms:
42 + -1[4 + -12 + 8y + -3y] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Combine like terms: 4 + -12 = -8
42 + -1[-8 + 8y + -3y] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Combine like terms: 8y + -3y = 5y
42 + -1[-8 + 5y] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]
42 + [-8 * -1 + 5y * -1] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]
42 + [8 + -5y] = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Combine like terms: 42 + 8 = 50
50 + -5y = -2(4y + -5) + -1[7(y + -1) + -1y + 3]

Reorder the terms:
50 + -5y = -2(-5 + 4y) + -1[7(y + -1) + -1y + 3]
50 + -5y = (-5 * -2 + 4y * -2) + -1[7(y + -1) + -1y + 3]
50 + -5y = (10 + -8y) + -1[7(y + -1) + -1y + 3]

Reorder the terms:
50 + -5y = 10 + -8y + -1[7(-1 + y) + -1y + 3]
50 + -5y = 10 + -8y + -1[(-1 * 7 + y * 7) + -1y + 3]
50 + -5y = 10 + -8y + -1[(-7 + 7y) + -1y + 3]

Reorder the terms:
50 + -5y = 10 + -8y + -1[-7 + 3 + 7y + -1y]

Combine like terms: -7 + 3 = -4
50 + -5y = 10 + -8y + -1[-4 + 7y + -1y]

Combine like terms: 7y + -1y = 6y
50 + -5y = 10 + -8y + -1[-4 + 6y]
50 + -5y = 10 + -8y + [-4 * -1 + 6y * -1]
50 + -5y = 10 + -8y + [4 + -6y]

Reorder the terms:
50 + -5y = 10 + 4 + -8y + -6y

Combine like terms: 10 + 4 = 14
50 + -5y = 14 + -8y + -6y

Combine like terms: -8y + -6y = -14y
50 + -5y = 14 + -14y

Solving
50 + -5y = 14 + -14y

Solving for variable 'y'.

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

Add '14y' to each side of the equation.
50 + -5y + 14y = 14 + -14y + 14y

Combine like terms: -5y + 14y = 9y
50 + 9y = 14 + -14y + 14y

Combine like terms: -14y + 14y = 0
50 + 9y = 14 + 0
50 + 9y = 14

Add '-50' to each side of the equation.
50 + -50 + 9y = 14 + -50

Combine like terms: 50 + -50 = 0
0 + 9y = 14 + -50
9y = 14 + -50

Combine like terms: 14 + -50 = -36
9y = -36

Divide each side by '9'.
y = -4

Simplifying
y = -4

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