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

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

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

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

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

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

Combine like terms: -2y + -4y = -6y
45 + -1[-24 + -6y] = [4 + -3(y + 2) + -2(2y + -5)]
45 + [-24 * -1 + -6y * -1] = [4 + -3(y + 2) + -2(2y + -5)]
45 + [24 + 6y] = [4 + -3(y + 2) + -2(2y + -5)]

Combine like terms: 45 + 24 = 69
69 + 6y = [4 + -3(y + 2) + -2(2y + -5)]

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

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

Reorder the terms:
69 + 6y = [4 + -6 + 10 + -3y + -4y]

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

Combine like terms: -2 + 10 = 8
69 + 6y = [8 + -3y + -4y]

Combine like terms: -3y + -4y = -7y
69 + 6y = [8 + -7y]

Remove brackets around [8 + -7y]
69 + 6y = 8 + -7y

Solving
69 + 6y = 8 + -7y

Solving for variable 'y'.

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

Add '7y' to each side of the equation.
69 + 6y + 7y = 8 + -7y + 7y

Combine like terms: 6y + 7y = 13y
69 + 13y = 8 + -7y + 7y

Combine like terms: -7y + 7y = 0
69 + 13y = 8 + 0
69 + 13y = 8

Add '-69' to each side of the equation.
69 + -69 + 13y = 8 + -69

Combine like terms: 69 + -69 = 0
0 + 13y = 8 + -69
13y = 8 + -69

Combine like terms: 8 + -69 = -61
13y = -61

Divide each side by '13'.
y = -4.692307692

Simplifying
y = -4.692307692