43-(5+6y-2(y+3))=3(2y-6)-(9(y-1)-6y+13)

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Solution for 43-(5+6y-2(y+3))=3(2y-6)-(9(y-1)-6y+13) equation: 


Simplifying
43 + -1(5 + 6y + -2(y + 3)) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Reorder the terms:
43 + -1(5 + 6y + -2(3 + y)) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)
43 + -1(5 + 6y + (3 * -2 + y * -2)) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)
43 + -1(5 + 6y + (-6 + -2y)) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Reorder the terms:
43 + -1(5 + -6 + 6y + -2y) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Combine like terms: 5 + -6 = -1
43 + -1(-1 + 6y + -2y) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Combine like terms: 6y + -2y = 4y
43 + -1(-1 + 4y) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)
43 + (-1 * -1 + 4y * -1) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)
43 + (1 + -4y) = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Combine like terms: 43 + 1 = 44
44 + -4y = 3(2y + -6) + -1(9(y + -1) + -6y + 13)

Reorder the terms:
44 + -4y = 3(-6 + 2y) + -1(9(y + -1) + -6y + 13)
44 + -4y = (-6 * 3 + 2y * 3) + -1(9(y + -1) + -6y + 13)
44 + -4y = (-18 + 6y) + -1(9(y + -1) + -6y + 13)

Reorder the terms:
44 + -4y = -18 + 6y + -1(9(-1 + y) + -6y + 13)
44 + -4y = -18 + 6y + -1((-1 * 9 + y * 9) + -6y + 13)
44 + -4y = -18 + 6y + -1((-9 + 9y) + -6y + 13)

Reorder the terms:
44 + -4y = -18 + 6y + -1(-9 + 13 + 9y + -6y)

Combine like terms: -9 + 13 = 4
44 + -4y = -18 + 6y + -1(4 + 9y + -6y)

Combine like terms: 9y + -6y = 3y
44 + -4y = -18 + 6y + -1(4 + 3y)
44 + -4y = -18 + 6y + (4 * -1 + 3y * -1)
44 + -4y = -18 + 6y + (-4 + -3y)

Reorder the terms:
44 + -4y = -18 + -4 + 6y + -3y

Combine like terms: -18 + -4 = -22
44 + -4y = -22 + 6y + -3y

Combine like terms: 6y + -3y = 3y
44 + -4y = -22 + 3y

Solving
44 + -4y = -22 + 3y

Solving for variable 'y'.

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

Add '-3y' to each side of the equation.
44 + -4y + -3y = -22 + 3y + -3y

Combine like terms: -4y + -3y = -7y
44 + -7y = -22 + 3y + -3y

Combine like terms: 3y + -3y = 0
44 + -7y = -22 + 0
44 + -7y = -22

Add '-44' to each side of the equation.
44 + -44 + -7y = -22 + -44

Combine like terms: 44 + -44 = 0
0 + -7y = -22 + -44
-7y = -22 + -44

Combine like terms: -22 + -44 = -66
-7y = -66

Divide each side by '-7'.
y = 9.428571429

Simplifying
y = 9.428571429

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