3y(-y+2)=(y-2)(y+2)-(2y+3)(2y-1)

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


Simplifying
3y(-1y + 2) = (y + -2)(y + 2) + -1(2y + 3)(2y + -1)

Reorder the terms:
3y(2 + -1y) = (y + -2)(y + 2) + -1(2y + 3)(2y + -1)
(2 * 3y + -1y * 3y) = (y + -2)(y + 2) + -1(2y + 3)(2y + -1)
(6y + -3y2) = (y + -2)(y + 2) + -1(2y + 3)(2y + -1)

Reorder the terms:
6y + -3y2 = (-2 + y)(y + 2) + -1(2y + 3)(2y + -1)

Reorder the terms:
6y + -3y2 = (-2 + y)(2 + y) + -1(2y + 3)(2y + -1)

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

Combine like terms: -2y + 2y = 0
6y + -3y2 = (-4 + 0 + y2) + -1(2y + 3)(2y + -1)
6y + -3y2 = (-4 + y2) + -1(2y + 3)(2y + -1)

Reorder the terms:
6y + -3y2 = -4 + y2 + -1(3 + 2y)(2y + -1)

Reorder the terms:
6y + -3y2 = -4 + y2 + -1(3 + 2y)(-1 + 2y)

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

Combine like terms: 6y + -2y = 4y
6y + -3y2 = -4 + y2 + -1(-3 + 4y + 4y2)
6y + -3y2 = -4 + y2 + (-3 * -1 + 4y * -1 + 4y2 * -1)
6y + -3y2 = -4 + y2 + (3 + -4y + -4y2)

Reorder the terms:
6y + -3y2 = -4 + 3 + -4y + y2 + -4y2

Combine like terms: -4 + 3 = -1
6y + -3y2 = -1 + -4y + y2 + -4y2

Combine like terms: y2 + -4y2 = -3y2
6y + -3y2 = -1 + -4y + -3y2

Add '3y2' to each side of the equation.
6y + -3y2 + 3y2 = -1 + -4y + -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
6y + 0 = -1 + -4y + -3y2 + 3y2
6y = -1 + -4y + -3y2 + 3y2

Combine like terms: -3y2 + 3y2 = 0
6y = -1 + -4y + 0
6y = -1 + -4y

Solving
6y = -1 + -4y

Solving for variable 'y'.

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

Add '4y' to each side of the equation.
6y + 4y = -1 + -4y + 4y

Combine like terms: 6y + 4y = 10y
10y = -1 + -4y + 4y

Combine like terms: -4y + 4y = 0
10y = -1 + 0
10y = -1

Divide each side by '10'.
y = -0.1

Simplifying
y = -0.1

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