-4(3Y+1)-(4-2(2Y-5)-3(Y+2))=45-(-2Y+4-4(Y+7))

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Solution for -4(3Y+1)-(4-2(2Y-5)-3(Y+2))=45-(-2Y+4-4(Y+7)) equation: 


Simplifying
-4(3Y + 1) + -1(4 + -2(2Y + -5) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-4(1 + 3Y) + -1(4 + -2(2Y + -5) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))
(1 * -4 + 3Y * -4) + -1(4 + -2(2Y + -5) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))
(-4 + -12Y) + -1(4 + -2(2Y + -5) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-4 + -12Y + -1(4 + -2(-5 + 2Y) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + -1(4 + (-5 * -2 + 2Y * -2) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + -1(4 + (10 + -4Y) + -3(Y + 2)) = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-4 + -12Y + -1(4 + 10 + -4Y + -3(2 + Y)) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + -1(4 + 10 + -4Y + (2 * -3 + Y * -3)) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + -1(4 + 10 + -4Y + (-6 + -3Y)) = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-4 + -12Y + -1(4 + 10 + -6 + -4Y + -3Y) = 45 + -1(-2Y + 4 + -4(Y + 7))

Combine like terms: 4 + 10 = 14
-4 + -12Y + -1(14 + -6 + -4Y + -3Y) = 45 + -1(-2Y + 4 + -4(Y + 7))

Combine like terms: 14 + -6 = 8
-4 + -12Y + -1(8 + -4Y + -3Y) = 45 + -1(-2Y + 4 + -4(Y + 7))

Combine like terms: -4Y + -3Y = -7Y
-4 + -12Y + -1(8 + -7Y) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + (8 * -1 + -7Y * -1) = 45 + -1(-2Y + 4 + -4(Y + 7))
-4 + -12Y + (-8 + 7Y) = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-4 + -8 + -12Y + 7Y = 45 + -1(-2Y + 4 + -4(Y + 7))

Combine like terms: -4 + -8 = -12
-12 + -12Y + 7Y = 45 + -1(-2Y + 4 + -4(Y + 7))

Combine like terms: -12Y + 7Y = -5Y
-12 + -5Y = 45 + -1(-2Y + 4 + -4(Y + 7))

Reorder the terms:
-12 + -5Y = 45 + -1(-2Y + 4 + -4(7 + Y))
-12 + -5Y = 45 + -1(-2Y + 4 + (7 * -4 + Y * -4))
-12 + -5Y = 45 + -1(-2Y + 4 + (-28 + -4Y))

Reorder the terms:
-12 + -5Y = 45 + -1(4 + -28 + -2Y + -4Y)

Combine like terms: 4 + -28 = -24
-12 + -5Y = 45 + -1(-24 + -2Y + -4Y)

Combine like terms: -2Y + -4Y = -6Y
-12 + -5Y = 45 + -1(-24 + -6Y)
-12 + -5Y = 45 + (-24 * -1 + -6Y * -1)
-12 + -5Y = 45 + (24 + 6Y)

Combine like terms: 45 + 24 = 69
-12 + -5Y = 69 + 6Y

Solving
-12 + -5Y = 69 + 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.
-12 + -5Y + -6Y = 69 + 6Y + -6Y

Combine like terms: -5Y + -6Y = -11Y
-12 + -11Y = 69 + 6Y + -6Y

Combine like terms: 6Y + -6Y = 0
-12 + -11Y = 69 + 0
-12 + -11Y = 69

Add '12' to each side of the equation.
-12 + 12 + -11Y = 69 + 12

Combine like terms: -12 + 12 = 0
0 + -11Y = 69 + 12
-11Y = 69 + 12

Combine like terms: 69 + 12 = 81
-11Y = 81

Divide each side by '-11'.
Y = -7.363636364

Simplifying
Y = -7.363636364

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