33-[1+8y-2(y+4)]=-4(5y-4)-[7(y-1)-12y+10]

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Solution for 33-[1+8y-2(y+4)]=-4(5y-4)-[7(y-1)-12y+10] equation: 


Simplifying
33 + -1[1 + 8y + -2(y + 4)] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Reorder the terms:
33 + -1[1 + 8y + -2(4 + y)] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]
33 + -1[1 + 8y + (4 * -2 + y * -2)] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]
33 + -1[1 + 8y + (-8 + -2y)] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Reorder the terms:
33 + -1[1 + -8 + 8y + -2y] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Combine like terms: 1 + -8 = -7
33 + -1[-7 + 8y + -2y] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Combine like terms: 8y + -2y = 6y
33 + -1[-7 + 6y] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]
33 + [-7 * -1 + 6y * -1] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]
33 + [7 + -6y] = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Combine like terms: 33 + 7 = 40
40 + -6y = -4(5y + -4) + -1[7(y + -1) + -12y + 10]

Reorder the terms:
40 + -6y = -4(-4 + 5y) + -1[7(y + -1) + -12y + 10]
40 + -6y = (-4 * -4 + 5y * -4) + -1[7(y + -1) + -12y + 10]
40 + -6y = (16 + -20y) + -1[7(y + -1) + -12y + 10]

Reorder the terms:
40 + -6y = 16 + -20y + -1[7(-1 + y) + -12y + 10]
40 + -6y = 16 + -20y + -1[(-1 * 7 + y * 7) + -12y + 10]
40 + -6y = 16 + -20y + -1[(-7 + 7y) + -12y + 10]

Reorder the terms:
40 + -6y = 16 + -20y + -1[-7 + 10 + 7y + -12y]

Combine like terms: -7 + 10 = 3
40 + -6y = 16 + -20y + -1[3 + 7y + -12y]

Combine like terms: 7y + -12y = -5y
40 + -6y = 16 + -20y + -1[3 + -5y]
40 + -6y = 16 + -20y + [3 * -1 + -5y * -1]
40 + -6y = 16 + -20y + [-3 + 5y]

Reorder the terms:
40 + -6y = 16 + -3 + -20y + 5y

Combine like terms: 16 + -3 = 13
40 + -6y = 13 + -20y + 5y

Combine like terms: -20y + 5y = -15y
40 + -6y = 13 + -15y

Solving
40 + -6y = 13 + -15y

Solving for variable 'y'.

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

Add '15y' to each side of the equation.
40 + -6y + 15y = 13 + -15y + 15y

Combine like terms: -6y + 15y = 9y
40 + 9y = 13 + -15y + 15y

Combine like terms: -15y + 15y = 0
40 + 9y = 13 + 0
40 + 9y = 13

Add '-40' to each side of the equation.
40 + -40 + 9y = 13 + -40

Combine like terms: 40 + -40 = 0
0 + 9y = 13 + -40
9y = 13 + -40

Combine like terms: 13 + -40 = -27
9y = -27

Divide each side by '9'.
y = -3

Simplifying
y = -3

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