40-[4+5y-2(y+4)]=-2(4y-5)-[7(y-1)-5y+1]

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Solution for 40-[4+5y-2(y+4)]=-2(4y-5)-[7(y-1)-5y+1] equation: 


Simplifying
40 + -1[4 + 5y + -2(y + 4)] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Reorder the terms:
40 + -1[4 + 5y + -2(4 + y)] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]
40 + -1[4 + 5y + (4 * -2 + y * -2)] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]
40 + -1[4 + 5y + (-8 + -2y)] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Reorder the terms:
40 + -1[4 + -8 + 5y + -2y] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Combine like terms: 4 + -8 = -4
40 + -1[-4 + 5y + -2y] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Combine like terms: 5y + -2y = 3y
40 + -1[-4 + 3y] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]
40 + [-4 * -1 + 3y * -1] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]
40 + [4 + -3y] = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Combine like terms: 40 + 4 = 44
44 + -3y = -2(4y + -5) + -1[7(y + -1) + -5y + 1]

Reorder the terms:
44 + -3y = -2(-5 + 4y) + -1[7(y + -1) + -5y + 1]
44 + -3y = (-5 * -2 + 4y * -2) + -1[7(y + -1) + -5y + 1]
44 + -3y = (10 + -8y) + -1[7(y + -1) + -5y + 1]

Reorder the terms:
44 + -3y = 10 + -8y + -1[7(-1 + y) + -5y + 1]
44 + -3y = 10 + -8y + -1[(-1 * 7 + y * 7) + -5y + 1]
44 + -3y = 10 + -8y + -1[(-7 + 7y) + -5y + 1]

Reorder the terms:
44 + -3y = 10 + -8y + -1[-7 + 1 + 7y + -5y]

Combine like terms: -7 + 1 = -6
44 + -3y = 10 + -8y + -1[-6 + 7y + -5y]

Combine like terms: 7y + -5y = 2y
44 + -3y = 10 + -8y + -1[-6 + 2y]
44 + -3y = 10 + -8y + [-6 * -1 + 2y * -1]
44 + -3y = 10 + -8y + [6 + -2y]

Reorder the terms:
44 + -3y = 10 + 6 + -8y + -2y

Combine like terms: 10 + 6 = 16
44 + -3y = 16 + -8y + -2y

Combine like terms: -8y + -2y = -10y
44 + -3y = 16 + -10y

Solving
44 + -3y = 16 + -10y

Solving for variable 'y'.

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

Add '10y' to each side of the equation.
44 + -3y + 10y = 16 + -10y + 10y

Combine like terms: -3y + 10y = 7y
44 + 7y = 16 + -10y + 10y

Combine like terms: -10y + 10y = 0
44 + 7y = 16 + 0
44 + 7y = 16

Add '-44' to each side of the equation.
44 + -44 + 7y = 16 + -44

Combine like terms: 44 + -44 = 0
0 + 7y = 16 + -44
7y = 16 + -44

Combine like terms: 16 + -44 = -28
7y = -28

Divide each side by '7'.
y = -4

Simplifying
y = -4

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