38-[2+6y-3(y+4)]=-3(5y-4)-[7(y-1)-12y+6]

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Solution for 38-[2+6y-3(y+4)]=-3(5y-4)-[7(y-1)-12y+6] equation: 


Simplifying
38 + -1[2 + 6y + -3(y + 4)] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Reorder the terms:
38 + -1[2 + 6y + -3(4 + y)] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]
38 + -1[2 + 6y + (4 * -3 + y * -3)] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]
38 + -1[2 + 6y + (-12 + -3y)] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Reorder the terms:
38 + -1[2 + -12 + 6y + -3y] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Combine like terms: 2 + -12 = -10
38 + -1[-10 + 6y + -3y] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Combine like terms: 6y + -3y = 3y
38 + -1[-10 + 3y] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]
38 + [-10 * -1 + 3y * -1] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]
38 + [10 + -3y] = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Combine like terms: 38 + 10 = 48
48 + -3y = -3(5y + -4) + -1[7(y + -1) + -12y + 6]

Reorder the terms:
48 + -3y = -3(-4 + 5y) + -1[7(y + -1) + -12y + 6]
48 + -3y = (-4 * -3 + 5y * -3) + -1[7(y + -1) + -12y + 6]
48 + -3y = (12 + -15y) + -1[7(y + -1) + -12y + 6]

Reorder the terms:
48 + -3y = 12 + -15y + -1[7(-1 + y) + -12y + 6]
48 + -3y = 12 + -15y + -1[(-1 * 7 + y * 7) + -12y + 6]
48 + -3y = 12 + -15y + -1[(-7 + 7y) + -12y + 6]

Reorder the terms:
48 + -3y = 12 + -15y + -1[-7 + 6 + 7y + -12y]

Combine like terms: -7 + 6 = -1
48 + -3y = 12 + -15y + -1[-1 + 7y + -12y]

Combine like terms: 7y + -12y = -5y
48 + -3y = 12 + -15y + -1[-1 + -5y]
48 + -3y = 12 + -15y + [-1 * -1 + -5y * -1]
48 + -3y = 12 + -15y + [1 + 5y]

Reorder the terms:
48 + -3y = 12 + 1 + -15y + 5y

Combine like terms: 12 + 1 = 13
48 + -3y = 13 + -15y + 5y

Combine like terms: -15y + 5y = -10y
48 + -3y = 13 + -10y

Solving
48 + -3y = 13 + -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.
48 + -3y + 10y = 13 + -10y + 10y

Combine like terms: -3y + 10y = 7y
48 + 7y = 13 + -10y + 10y

Combine like terms: -10y + 10y = 0
48 + 7y = 13 + 0
48 + 7y = 13

Add '-48' to each side of the equation.
48 + -48 + 7y = 13 + -48

Combine like terms: 48 + -48 = 0
0 + 7y = 13 + -48
7y = 13 + -48

Combine like terms: 13 + -48 = -35
7y = -35

Divide each side by '7'.
y = -5

Simplifying
y = -5

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