45-[4+8y-3(y+3)]=-5(3y-4)-[7(y-1)-11y+13]

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Solution for 45-[4+8y-3(y+3)]=-5(3y-4)-[7(y-1)-11y+13] equation:


Simplifying
45 + -1[4 + 8y + -3(y + 3)] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Reorder the terms:
45 + -1[4 + 8y + -3(3 + y)] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]
45 + -1[4 + 8y + (3 * -3 + y * -3)] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]
45 + -1[4 + 8y + (-9 + -3y)] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Reorder the terms:
45 + -1[4 + -9 + 8y + -3y] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Combine like terms: 4 + -9 = -5
45 + -1[-5 + 8y + -3y] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Combine like terms: 8y + -3y = 5y
45 + -1[-5 + 5y] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]
45 + [-5 * -1 + 5y * -1] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]
45 + [5 + -5y] = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Combine like terms: 45 + 5 = 50
50 + -5y = -5(3y + -4) + -1[7(y + -1) + -11y + 13]

Reorder the terms:
50 + -5y = -5(-4 + 3y) + -1[7(y + -1) + -11y + 13]
50 + -5y = (-4 * -5 + 3y * -5) + -1[7(y + -1) + -11y + 13]
50 + -5y = (20 + -15y) + -1[7(y + -1) + -11y + 13]

Reorder the terms:
50 + -5y = 20 + -15y + -1[7(-1 + y) + -11y + 13]
50 + -5y = 20 + -15y + -1[(-1 * 7 + y * 7) + -11y + 13]
50 + -5y = 20 + -15y + -1[(-7 + 7y) + -11y + 13]

Reorder the terms:
50 + -5y = 20 + -15y + -1[-7 + 13 + 7y + -11y]

Combine like terms: -7 + 13 = 6
50 + -5y = 20 + -15y + -1[6 + 7y + -11y]

Combine like terms: 7y + -11y = -4y
50 + -5y = 20 + -15y + -1[6 + -4y]
50 + -5y = 20 + -15y + [6 * -1 + -4y * -1]
50 + -5y = 20 + -15y + [-6 + 4y]

Reorder the terms:
50 + -5y = 20 + -6 + -15y + 4y

Combine like terms: 20 + -6 = 14
50 + -5y = 14 + -15y + 4y

Combine like terms: -15y + 4y = -11y
50 + -5y = 14 + -11y

Solving
50 + -5y = 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.
50 + -5y + 11y = 14 + -11y + 11y

Combine like terms: -5y + 11y = 6y
50 + 6y = 14 + -11y + 11y

Combine like terms: -11y + 11y = 0
50 + 6y = 14 + 0
50 + 6y = 14

Add '-50' to each side of the equation.
50 + -50 + 6y = 14 + -50

Combine like terms: 50 + -50 = 0
0 + 6y = 14 + -50
6y = 14 + -50

Combine like terms: 14 + -50 = -36
6y = -36

Divide each side by '6'.
y = -6

Simplifying
y = -6

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