5(y+2)(2y+3)-2(y-1)(5y-4)=75

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Solution for 5(y+2)(2y+3)-2(y-1)(5y-4)=75 equation: 


Simplifying
5(y + 2)(2y + 3) + -2(y + -1)(5y + -4) = 75

Reorder the terms:
5(2 + y)(2y + 3) + -2(y + -1)(5y + -4) = 75

Reorder the terms:
5(2 + y)(3 + 2y) + -2(y + -1)(5y + -4) = 75

Multiply (2 + y) * (3 + 2y)
5(2(3 + 2y) + y(3 + 2y)) + -2(y + -1)(5y + -4) = 75
5((3 * 2 + 2y * 2) + y(3 + 2y)) + -2(y + -1)(5y + -4) = 75
5((6 + 4y) + y(3 + 2y)) + -2(y + -1)(5y + -4) = 75
5(6 + 4y + (3 * y + 2y * y)) + -2(y + -1)(5y + -4) = 75
5(6 + 4y + (3y + 2y2)) + -2(y + -1)(5y + -4) = 75

Combine like terms: 4y + 3y = 7y
5(6 + 7y + 2y2) + -2(y + -1)(5y + -4) = 75
(6 * 5 + 7y * 5 + 2y2 * 5) + -2(y + -1)(5y + -4) = 75
(30 + 35y + 10y2) + -2(y + -1)(5y + -4) = 75

Reorder the terms:
30 + 35y + 10y2 + -2(-1 + y)(5y + -4) = 75

Reorder the terms:
30 + 35y + 10y2 + -2(-1 + y)(-4 + 5y) = 75

Multiply (-1 + y) * (-4 + 5y)
30 + 35y + 10y2 + -2(-1(-4 + 5y) + y(-4 + 5y)) = 75
30 + 35y + 10y2 + -2((-4 * -1 + 5y * -1) + y(-4 + 5y)) = 75
30 + 35y + 10y2 + -2((4 + -5y) + y(-4 + 5y)) = 75
30 + 35y + 10y2 + -2(4 + -5y + (-4 * y + 5y * y)) = 75
30 + 35y + 10y2 + -2(4 + -5y + (-4y + 5y2)) = 75

Combine like terms: -5y + -4y = -9y
30 + 35y + 10y2 + -2(4 + -9y + 5y2) = 75
30 + 35y + 10y2 + (4 * -2 + -9y * -2 + 5y2 * -2) = 75
30 + 35y + 10y2 + (-8 + 18y + -10y2) = 75

Reorder the terms:
30 + -8 + 35y + 18y + 10y2 + -10y2 = 75

Combine like terms: 30 + -8 = 22
22 + 35y + 18y + 10y2 + -10y2 = 75

Combine like terms: 35y + 18y = 53y
22 + 53y + 10y2 + -10y2 = 75

Combine like terms: 10y2 + -10y2 = 0
22 + 53y + 0 = 75
22 + 53y = 75

Solving
22 + 53y = 75

Solving for variable 'y'.

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

Add '-22' to each side of the equation.
22 + -22 + 53y = 75 + -22

Combine like terms: 22 + -22 = 0
0 + 53y = 75 + -22
53y = 75 + -22

Combine like terms: 75 + -22 = 53
53y = 53

Divide each side by '53'.
y = 1

Simplifying
y = 1

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