19-[3+7y-4(y+4)]=-5(4y-3)-[7(y-1)-21y+11]

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Solution for 19-[3+7y-4(y+4)]=-5(4y-3)-[7(y-1)-21y+11] equation:


Simplifying
19 + -1[3 + 7y + -4(y + 4)] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Reorder the terms:
19 + -1[3 + 7y + -4(4 + y)] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]
19 + -1[3 + 7y + (4 * -4 + y * -4)] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]
19 + -1[3 + 7y + (-16 + -4y)] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Reorder the terms:
19 + -1[3 + -16 + 7y + -4y] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Combine like terms: 3 + -16 = -13
19 + -1[-13 + 7y + -4y] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Combine like terms: 7y + -4y = 3y
19 + -1[-13 + 3y] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]
19 + [-13 * -1 + 3y * -1] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]
19 + [13 + -3y] = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Combine like terms: 19 + 13 = 32
32 + -3y = -5(4y + -3) + -1[7(y + -1) + -21y + 11]

Reorder the terms:
32 + -3y = -5(-3 + 4y) + -1[7(y + -1) + -21y + 11]
32 + -3y = (-3 * -5 + 4y * -5) + -1[7(y + -1) + -21y + 11]
32 + -3y = (15 + -20y) + -1[7(y + -1) + -21y + 11]

Reorder the terms:
32 + -3y = 15 + -20y + -1[7(-1 + y) + -21y + 11]
32 + -3y = 15 + -20y + -1[(-1 * 7 + y * 7) + -21y + 11]
32 + -3y = 15 + -20y + -1[(-7 + 7y) + -21y + 11]

Reorder the terms:
32 + -3y = 15 + -20y + -1[-7 + 11 + 7y + -21y]

Combine like terms: -7 + 11 = 4
32 + -3y = 15 + -20y + -1[4 + 7y + -21y]

Combine like terms: 7y + -21y = -14y
32 + -3y = 15 + -20y + -1[4 + -14y]
32 + -3y = 15 + -20y + [4 * -1 + -14y * -1]
32 + -3y = 15 + -20y + [-4 + 14y]

Reorder the terms:
32 + -3y = 15 + -4 + -20y + 14y

Combine like terms: 15 + -4 = 11
32 + -3y = 11 + -20y + 14y

Combine like terms: -20y + 14y = -6y
32 + -3y = 11 + -6y

Solving
32 + -3y = 11 + -6y

Solving for variable 'y'.

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

Add '6y' to each side of the equation.
32 + -3y + 6y = 11 + -6y + 6y

Combine like terms: -3y + 6y = 3y
32 + 3y = 11 + -6y + 6y

Combine like terms: -6y + 6y = 0
32 + 3y = 11 + 0
32 + 3y = 11

Add '-32' to each side of the equation.
32 + -32 + 3y = 11 + -32

Combine like terms: 32 + -32 = 0
0 + 3y = 11 + -32
3y = 11 + -32

Combine like terms: 11 + -32 = -21
3y = -21

Divide each side by '3'.
y = -7

Simplifying
y = -7

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