10(2y+1)+3(-5y-3)+9=-8(2-2y)+2(-7y+10)

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Solution for 10(2y+1)+3(-5y-3)+9=-8(2-2y)+2(-7y+10) equation: 


Simplifying
10(2y + 1) + 3(-5y + -3) + 9 = -8(2 + -2y) + 2(-7y + 10)

Reorder the terms:
10(1 + 2y) + 3(-5y + -3) + 9 = -8(2 + -2y) + 2(-7y + 10)
(1 * 10 + 2y * 10) + 3(-5y + -3) + 9 = -8(2 + -2y) + 2(-7y + 10)
(10 + 20y) + 3(-5y + -3) + 9 = -8(2 + -2y) + 2(-7y + 10)

Reorder the terms:
10 + 20y + 3(-3 + -5y) + 9 = -8(2 + -2y) + 2(-7y + 10)
10 + 20y + (-3 * 3 + -5y * 3) + 9 = -8(2 + -2y) + 2(-7y + 10)
10 + 20y + (-9 + -15y) + 9 = -8(2 + -2y) + 2(-7y + 10)

Reorder the terms:
10 + -9 + 9 + 20y + -15y = -8(2 + -2y) + 2(-7y + 10)

Combine like terms: 10 + -9 = 1
1 + 9 + 20y + -15y = -8(2 + -2y) + 2(-7y + 10)

Combine like terms: 1 + 9 = 10
10 + 20y + -15y = -8(2 + -2y) + 2(-7y + 10)

Combine like terms: 20y + -15y = 5y
10 + 5y = -8(2 + -2y) + 2(-7y + 10)
10 + 5y = (2 * -8 + -2y * -8) + 2(-7y + 10)
10 + 5y = (-16 + 16y) + 2(-7y + 10)

Reorder the terms:
10 + 5y = -16 + 16y + 2(10 + -7y)
10 + 5y = -16 + 16y + (10 * 2 + -7y * 2)
10 + 5y = -16 + 16y + (20 + -14y)

Reorder the terms:
10 + 5y = -16 + 20 + 16y + -14y

Combine like terms: -16 + 20 = 4
10 + 5y = 4 + 16y + -14y

Combine like terms: 16y + -14y = 2y
10 + 5y = 4 + 2y

Solving
10 + 5y = 4 + 2y

Solving for variable 'y'.

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

Add '-2y' to each side of the equation.
10 + 5y + -2y = 4 + 2y + -2y

Combine like terms: 5y + -2y = 3y
10 + 3y = 4 + 2y + -2y

Combine like terms: 2y + -2y = 0
10 + 3y = 4 + 0
10 + 3y = 4

Add '-10' to each side of the equation.
10 + -10 + 3y = 4 + -10

Combine like terms: 10 + -10 = 0
0 + 3y = 4 + -10
3y = 4 + -10

Combine like terms: 4 + -10 = -6
3y = -6

Divide each side by '3'.
y = -2

Simplifying
y = -2

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