31-[1+6y-3(y+5)]=-3(3y-7)-[7(y-1)-5y+15]

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Solution for 31-[1+6y-3(y+5)]=-3(3y-7)-[7(y-1)-5y+15] equation:


Simplifying
31 + -1[1 + 6y + -3(y + 5)] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Reorder the terms:
31 + -1[1 + 6y + -3(5 + y)] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]
31 + -1[1 + 6y + (5 * -3 + y * -3)] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]
31 + -1[1 + 6y + (-15 + -3y)] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Reorder the terms:
31 + -1[1 + -15 + 6y + -3y] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Combine like terms: 1 + -15 = -14
31 + -1[-14 + 6y + -3y] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Combine like terms: 6y + -3y = 3y
31 + -1[-14 + 3y] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]
31 + [-14 * -1 + 3y * -1] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]
31 + [14 + -3y] = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Combine like terms: 31 + 14 = 45
45 + -3y = -3(3y + -7) + -1[7(y + -1) + -5y + 15]

Reorder the terms:
45 + -3y = -3(-7 + 3y) + -1[7(y + -1) + -5y + 15]
45 + -3y = (-7 * -3 + 3y * -3) + -1[7(y + -1) + -5y + 15]
45 + -3y = (21 + -9y) + -1[7(y + -1) + -5y + 15]

Reorder the terms:
45 + -3y = 21 + -9y + -1[7(-1 + y) + -5y + 15]
45 + -3y = 21 + -9y + -1[(-1 * 7 + y * 7) + -5y + 15]
45 + -3y = 21 + -9y + -1[(-7 + 7y) + -5y + 15]

Reorder the terms:
45 + -3y = 21 + -9y + -1[-7 + 15 + 7y + -5y]

Combine like terms: -7 + 15 = 8
45 + -3y = 21 + -9y + -1[8 + 7y + -5y]

Combine like terms: 7y + -5y = 2y
45 + -3y = 21 + -9y + -1[8 + 2y]
45 + -3y = 21 + -9y + [8 * -1 + 2y * -1]
45 + -3y = 21 + -9y + [-8 + -2y]

Reorder the terms:
45 + -3y = 21 + -8 + -9y + -2y

Combine like terms: 21 + -8 = 13
45 + -3y = 13 + -9y + -2y

Combine like terms: -9y + -2y = -11y
45 + -3y = 13 + -11y

Solving
45 + -3y = 13 + -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.
45 + -3y + 11y = 13 + -11y + 11y

Combine like terms: -3y + 11y = 8y
45 + 8y = 13 + -11y + 11y

Combine like terms: -11y + 11y = 0
45 + 8y = 13 + 0
45 + 8y = 13

Add '-45' to each side of the equation.
45 + -45 + 8y = 13 + -45

Combine like terms: 45 + -45 = 0
0 + 8y = 13 + -45
8y = 13 + -45

Combine like terms: 13 + -45 = -32
8y = -32

Divide each side by '8'.
y = -4

Simplifying
y = -4

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