31-[3+6y-3(y+2)]=-2(3y-5)-[7(y-1)-4y+1]

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Solution for 31-[3+6y-3(y+2)]=-2(3y-5)-[7(y-1)-4y+1] equation: 


Simplifying
31 + -1[3 + 6y + -3(y + 2)] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Reorder the terms:
31 + -1[3 + 6y + -3(2 + y)] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]
31 + -1[3 + 6y + (2 * -3 + y * -3)] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]
31 + -1[3 + 6y + (-6 + -3y)] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Reorder the terms:
31 + -1[3 + -6 + 6y + -3y] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Combine like terms: 3 + -6 = -3
31 + -1[-3 + 6y + -3y] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Combine like terms: 6y + -3y = 3y
31 + -1[-3 + 3y] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]
31 + [-3 * -1 + 3y * -1] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]
31 + [3 + -3y] = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Combine like terms: 31 + 3 = 34
34 + -3y = -2(3y + -5) + -1[7(y + -1) + -4y + 1]

Reorder the terms:
34 + -3y = -2(-5 + 3y) + -1[7(y + -1) + -4y + 1]
34 + -3y = (-5 * -2 + 3y * -2) + -1[7(y + -1) + -4y + 1]
34 + -3y = (10 + -6y) + -1[7(y + -1) + -4y + 1]

Reorder the terms:
34 + -3y = 10 + -6y + -1[7(-1 + y) + -4y + 1]
34 + -3y = 10 + -6y + -1[(-1 * 7 + y * 7) + -4y + 1]
34 + -3y = 10 + -6y + -1[(-7 + 7y) + -4y + 1]

Reorder the terms:
34 + -3y = 10 + -6y + -1[-7 + 1 + 7y + -4y]

Combine like terms: -7 + 1 = -6
34 + -3y = 10 + -6y + -1[-6 + 7y + -4y]

Combine like terms: 7y + -4y = 3y
34 + -3y = 10 + -6y + -1[-6 + 3y]
34 + -3y = 10 + -6y + [-6 * -1 + 3y * -1]
34 + -3y = 10 + -6y + [6 + -3y]

Reorder the terms:
34 + -3y = 10 + 6 + -6y + -3y

Combine like terms: 10 + 6 = 16
34 + -3y = 16 + -6y + -3y

Combine like terms: -6y + -3y = -9y
34 + -3y = 16 + -9y

Solving
34 + -3y = 16 + -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.
34 + -3y + 9y = 16 + -9y + 9y

Combine like terms: -3y + 9y = 6y
34 + 6y = 16 + -9y + 9y

Combine like terms: -9y + 9y = 0
34 + 6y = 16 + 0
34 + 6y = 16

Add '-34' to each side of the equation.
34 + -34 + 6y = 16 + -34

Combine like terms: 34 + -34 = 0
0 + 6y = 16 + -34
6y = 16 + -34

Combine like terms: 16 + -34 = -18
6y = -18

Divide each side by '6'.
y = -3

Simplifying
y = -3

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