5-[1+10y-4(y+5)]=-5(4y-7)-[7(y-1)-16y+28]

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Solution for 5-[1+10y-4(y+5)]=-5(4y-7)-[7(y-1)-16y+28] equation:


Simplifying
5 + -1[1 + 10y + -4(y + 5)] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Reorder the terms:
5 + -1[1 + 10y + -4(5 + y)] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]
5 + -1[1 + 10y + (5 * -4 + y * -4)] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]
5 + -1[1 + 10y + (-20 + -4y)] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Reorder the terms:
5 + -1[1 + -20 + 10y + -4y] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Combine like terms: 1 + -20 = -19
5 + -1[-19 + 10y + -4y] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Combine like terms: 10y + -4y = 6y
5 + -1[-19 + 6y] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]
5 + [-19 * -1 + 6y * -1] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]
5 + [19 + -6y] = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Combine like terms: 5 + 19 = 24
24 + -6y = -5(4y + -7) + -1[7(y + -1) + -16y + 28]

Reorder the terms:
24 + -6y = -5(-7 + 4y) + -1[7(y + -1) + -16y + 28]
24 + -6y = (-7 * -5 + 4y * -5) + -1[7(y + -1) + -16y + 28]
24 + -6y = (35 + -20y) + -1[7(y + -1) + -16y + 28]

Reorder the terms:
24 + -6y = 35 + -20y + -1[7(-1 + y) + -16y + 28]
24 + -6y = 35 + -20y + -1[(-1 * 7 + y * 7) + -16y + 28]
24 + -6y = 35 + -20y + -1[(-7 + 7y) + -16y + 28]

Reorder the terms:
24 + -6y = 35 + -20y + -1[-7 + 28 + 7y + -16y]

Combine like terms: -7 + 28 = 21
24 + -6y = 35 + -20y + -1[21 + 7y + -16y]

Combine like terms: 7y + -16y = -9y
24 + -6y = 35 + -20y + -1[21 + -9y]
24 + -6y = 35 + -20y + [21 * -1 + -9y * -1]
24 + -6y = 35 + -20y + [-21 + 9y]

Reorder the terms:
24 + -6y = 35 + -21 + -20y + 9y

Combine like terms: 35 + -21 = 14
24 + -6y = 14 + -20y + 9y

Combine like terms: -20y + 9y = -11y
24 + -6y = 14 + -11y

Solving
24 + -6y = 14 + -11y

Solving for variable 'y'.

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

Add '11y' to each side of the equation.
24 + -6y + 11y = 14 + -11y + 11y

Combine like terms: -6y + 11y = 5y
24 + 5y = 14 + -11y + 11y

Combine like terms: -11y + 11y = 0
24 + 5y = 14 + 0
24 + 5y = 14

Add '-24' to each side of the equation.
24 + -24 + 5y = 14 + -24

Combine like terms: 24 + -24 = 0
0 + 5y = 14 + -24
5y = 14 + -24

Combine like terms: 14 + -24 = -10
5y = -10

Divide each side by '5'.
y = -2

Simplifying
y = -2

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