52-[5+6y-3(y+4)]=-4(3y-3)-[8(y-1)-10y+3]

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Solution for 52-[5+6y-3(y+4)]=-4(3y-3)-[8(y-1)-10y+3] equation: 


Simplifying
52 + -1[5 + 6y + -3(y + 4)] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Reorder the terms:
52 + -1[5 + 6y + -3(4 + y)] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]
52 + -1[5 + 6y + (4 * -3 + y * -3)] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]
52 + -1[5 + 6y + (-12 + -3y)] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Reorder the terms:
52 + -1[5 + -12 + 6y + -3y] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Combine like terms: 5 + -12 = -7
52 + -1[-7 + 6y + -3y] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Combine like terms: 6y + -3y = 3y
52 + -1[-7 + 3y] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]
52 + [-7 * -1 + 3y * -1] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]
52 + [7 + -3y] = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Combine like terms: 52 + 7 = 59
59 + -3y = -4(3y + -3) + -1[8(y + -1) + -10y + 3]

Reorder the terms:
59 + -3y = -4(-3 + 3y) + -1[8(y + -1) + -10y + 3]
59 + -3y = (-3 * -4 + 3y * -4) + -1[8(y + -1) + -10y + 3]
59 + -3y = (12 + -12y) + -1[8(y + -1) + -10y + 3]

Reorder the terms:
59 + -3y = 12 + -12y + -1[8(-1 + y) + -10y + 3]
59 + -3y = 12 + -12y + -1[(-1 * 8 + y * 8) + -10y + 3]
59 + -3y = 12 + -12y + -1[(-8 + 8y) + -10y + 3]

Reorder the terms:
59 + -3y = 12 + -12y + -1[-8 + 3 + 8y + -10y]

Combine like terms: -8 + 3 = -5
59 + -3y = 12 + -12y + -1[-5 + 8y + -10y]

Combine like terms: 8y + -10y = -2y
59 + -3y = 12 + -12y + -1[-5 + -2y]
59 + -3y = 12 + -12y + [-5 * -1 + -2y * -1]
59 + -3y = 12 + -12y + [5 + 2y]

Reorder the terms:
59 + -3y = 12 + 5 + -12y + 2y

Combine like terms: 12 + 5 = 17
59 + -3y = 17 + -12y + 2y

Combine like terms: -12y + 2y = -10y
59 + -3y = 17 + -10y

Solving
59 + -3y = 17 + -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.
59 + -3y + 10y = 17 + -10y + 10y

Combine like terms: -3y + 10y = 7y
59 + 7y = 17 + -10y + 10y

Combine like terms: -10y + 10y = 0
59 + 7y = 17 + 0
59 + 7y = 17

Add '-59' to each side of the equation.
59 + -59 + 7y = 17 + -59

Combine like terms: 59 + -59 = 0
0 + 7y = 17 + -59
7y = 17 + -59

Combine like terms: 17 + -59 = -42
7y = -42

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

Simplifying
y = -6

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