46-[2+6y-4(y+4)]=-4(2y-3)-[7(y-1)-6y+1]

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Solution for 46-[2+6y-4(y+4)]=-4(2y-3)-[7(y-1)-6y+1] equation:


Simplifying
46 + -1[2 + 6y + -4(y + 4)] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Reorder the terms:
46 + -1[2 + 6y + -4(4 + y)] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]
46 + -1[2 + 6y + (4 * -4 + y * -4)] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]
46 + -1[2 + 6y + (-16 + -4y)] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Reorder the terms:
46 + -1[2 + -16 + 6y + -4y] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Combine like terms: 2 + -16 = -14
46 + -1[-14 + 6y + -4y] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Combine like terms: 6y + -4y = 2y
46 + -1[-14 + 2y] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]
46 + [-14 * -1 + 2y * -1] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]
46 + [14 + -2y] = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Combine like terms: 46 + 14 = 60
60 + -2y = -4(2y + -3) + -1[7(y + -1) + -6y + 1]

Reorder the terms:
60 + -2y = -4(-3 + 2y) + -1[7(y + -1) + -6y + 1]
60 + -2y = (-3 * -4 + 2y * -4) + -1[7(y + -1) + -6y + 1]
60 + -2y = (12 + -8y) + -1[7(y + -1) + -6y + 1]

Reorder the terms:
60 + -2y = 12 + -8y + -1[7(-1 + y) + -6y + 1]
60 + -2y = 12 + -8y + -1[(-1 * 7 + y * 7) + -6y + 1]
60 + -2y = 12 + -8y + -1[(-7 + 7y) + -6y + 1]

Reorder the terms:
60 + -2y = 12 + -8y + -1[-7 + 1 + 7y + -6y]

Combine like terms: -7 + 1 = -6
60 + -2y = 12 + -8y + -1[-6 + 7y + -6y]

Combine like terms: 7y + -6y = 1y
60 + -2y = 12 + -8y + -1[-6 + 1y]
60 + -2y = 12 + -8y + [-6 * -1 + 1y * -1]
60 + -2y = 12 + -8y + [6 + -1y]

Reorder the terms:
60 + -2y = 12 + 6 + -8y + -1y

Combine like terms: 12 + 6 = 18
60 + -2y = 18 + -8y + -1y

Combine like terms: -8y + -1y = -9y
60 + -2y = 18 + -9y

Solving
60 + -2y = 18 + -9y

Solving for variable 'y'.

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

Add '9y' to each side of the equation.
60 + -2y + 9y = 18 + -9y + 9y

Combine like terms: -2y + 9y = 7y
60 + 7y = 18 + -9y + 9y

Combine like terms: -9y + 9y = 0
60 + 7y = 18 + 0
60 + 7y = 18

Add '-60' to each side of the equation.
60 + -60 + 7y = 18 + -60

Combine like terms: 60 + -60 = 0
0 + 7y = 18 + -60
7y = 18 + -60

Combine like terms: 18 + -60 = -42
7y = -42

Divide each side by '7'.
y = -6

Simplifying
y = -6

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