19-(3+6y-4(y+4))=-3(2y-6)-(7(y-1)-6y+13)

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Solution for 19-(3+6y-4(y+4))=-3(2y-6)-(7(y-1)-6y+13) equation: 


Simplifying
19 + -1(3 + 6y + -4(y + 4)) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Reorder the terms:
19 + -1(3 + 6y + -4(4 + y)) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)
19 + -1(3 + 6y + (4 * -4 + y * -4)) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)
19 + -1(3 + 6y + (-16 + -4y)) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Reorder the terms:
19 + -1(3 + -16 + 6y + -4y) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Combine like terms: 3 + -16 = -13
19 + -1(-13 + 6y + -4y) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Combine like terms: 6y + -4y = 2y
19 + -1(-13 + 2y) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)
19 + (-13 * -1 + 2y * -1) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)
19 + (13 + -2y) = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Combine like terms: 19 + 13 = 32
32 + -2y = -3(2y + -6) + -1(7(y + -1) + -6y + 13)

Reorder the terms:
32 + -2y = -3(-6 + 2y) + -1(7(y + -1) + -6y + 13)
32 + -2y = (-6 * -3 + 2y * -3) + -1(7(y + -1) + -6y + 13)
32 + -2y = (18 + -6y) + -1(7(y + -1) + -6y + 13)

Reorder the terms:
32 + -2y = 18 + -6y + -1(7(-1 + y) + -6y + 13)
32 + -2y = 18 + -6y + -1((-1 * 7 + y * 7) + -6y + 13)
32 + -2y = 18 + -6y + -1((-7 + 7y) + -6y + 13)

Reorder the terms:
32 + -2y = 18 + -6y + -1(-7 + 13 + 7y + -6y)

Combine like terms: -7 + 13 = 6
32 + -2y = 18 + -6y + -1(6 + 7y + -6y)

Combine like terms: 7y + -6y = 1y
32 + -2y = 18 + -6y + -1(6 + 1y)
32 + -2y = 18 + -6y + (6 * -1 + 1y * -1)
32 + -2y = 18 + -6y + (-6 + -1y)

Reorder the terms:
32 + -2y = 18 + -6 + -6y + -1y

Combine like terms: 18 + -6 = 12
32 + -2y = 12 + -6y + -1y

Combine like terms: -6y + -1y = -7y
32 + -2y = 12 + -7y

Solving
32 + -2y = 12 + -7y

Solving for variable 'y'.

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

Add '7y' to each side of the equation.
32 + -2y + 7y = 12 + -7y + 7y

Combine like terms: -2y + 7y = 5y
32 + 5y = 12 + -7y + 7y

Combine like terms: -7y + 7y = 0
32 + 5y = 12 + 0
32 + 5y = 12

Add '-32' to each side of the equation.
32 + -32 + 5y = 12 + -32

Combine like terms: 32 + -32 = 0
0 + 5y = 12 + -32
5y = 12 + -32

Combine like terms: 12 + -32 = -20
5y = -20

Divide each side by '5'.
y = -4

Simplifying
y = -4

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