45-[4-2x-4(y+7)]=-4(1+3y)-[4-3(y+2)-2(2y-5)]

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Solution for 45-[4-2x-4(y+7)]=-4(1+3y)-[4-3(y+2)-2(2y-5)] equation: 


Simplifying
45 + -1[4 + -2x + -4(y + 7)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
45 + -1[4 + -2x + -4(7 + y)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + -1[4 + -2x + (7 * -4 + y * -4)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + -1[4 + -2x + (-28 + -4y)] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
45 + -1[4 + -28 + -2x + -4y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Combine like terms: 4 + -28 = -24
45 + -1[-24 + -2x + -4y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + [-24 * -1 + -2x * -1 + -4y * -1] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
45 + [24 + 2x + 4y] = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Combine like terms: 45 + 24 = 69
69 + 2x + 4y = -4(1 + 3y) + -1[4 + -3(y + 2) + -2(2y + -5)]
69 + 2x + 4y = (1 * -4 + 3y * -4) + -1[4 + -3(y + 2) + -2(2y + -5)]
69 + 2x + 4y = (-4 + -12y) + -1[4 + -3(y + 2) + -2(2y + -5)]

Reorder the terms:
69 + 2x + 4y = -4 + -12y + -1[4 + -3(2 + y) + -2(2y + -5)]
69 + 2x + 4y = -4 + -12y + -1[4 + (2 * -3 + y * -3) + -2(2y + -5)]
69 + 2x + 4y = -4 + -12y + -1[4 + (-6 + -3y) + -2(2y + -5)]

Reorder the terms:
69 + 2x + 4y = -4 + -12y + -1[4 + -6 + -3y + -2(-5 + 2y)]
69 + 2x + 4y = -4 + -12y + -1[4 + -6 + -3y + (-5 * -2 + 2y * -2)]
69 + 2x + 4y = -4 + -12y + -1[4 + -6 + -3y + (10 + -4y)]

Reorder the terms:
69 + 2x + 4y = -4 + -12y + -1[4 + -6 + 10 + -3y + -4y]

Combine like terms: 4 + -6 = -2
69 + 2x + 4y = -4 + -12y + -1[-2 + 10 + -3y + -4y]

Combine like terms: -2 + 10 = 8
69 + 2x + 4y = -4 + -12y + -1[8 + -3y + -4y]

Combine like terms: -3y + -4y = -7y
69 + 2x + 4y = -4 + -12y + -1[8 + -7y]
69 + 2x + 4y = -4 + -12y + [8 * -1 + -7y * -1]
69 + 2x + 4y = -4 + -12y + [-8 + 7y]

Reorder the terms:
69 + 2x + 4y = -4 + -8 + -12y + 7y

Combine like terms: -4 + -8 = -12
69 + 2x + 4y = -12 + -12y + 7y

Combine like terms: -12y + 7y = -5y
69 + 2x + 4y = -12 + -5y

Solving
69 + 2x + 4y = -12 + -5y

Solving for variable 'x'.

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

Add '-69' to each side of the equation.
69 + 2x + -69 + 4y = -12 + -69 + -5y

Reorder the terms:
69 + -69 + 2x + 4y = -12 + -69 + -5y

Combine like terms: 69 + -69 = 0
0 + 2x + 4y = -12 + -69 + -5y
2x + 4y = -12 + -69 + -5y

Combine like terms: -12 + -69 = -81
2x + 4y = -81 + -5y

Add '-4y' to each side of the equation.
2x + 4y + -4y = -81 + -5y + -4y

Combine like terms: 4y + -4y = 0
2x + 0 = -81 + -5y + -4y
2x = -81 + -5y + -4y

Combine like terms: -5y + -4y = -9y
2x = -81 + -9y

Divide each side by '2'.
x = -40.5 + -4.5y

Simplifying
x = -40.5 + -4.5y

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