(2y+1)(y-1)=(y+5)(2y-5)

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


Simplifying
(2y + 1)(y + -1) = (y + 5)(2y + -5)

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

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

Multiply (1 + 2y) * (-1 + y)
(1(-1 + y) + 2y * (-1 + y)) = (y + 5)(2y + -5)
((-1 * 1 + y * 1) + 2y * (-1 + y)) = (y + 5)(2y + -5)
((-1 + 1y) + 2y * (-1 + y)) = (y + 5)(2y + -5)
(-1 + 1y + (-1 * 2y + y * 2y)) = (y + 5)(2y + -5)
(-1 + 1y + (-2y + 2y2)) = (y + 5)(2y + -5)

Combine like terms: 1y + -2y = -1y
(-1 + -1y + 2y2) = (y + 5)(2y + -5)

Reorder the terms:
-1 + -1y + 2y2 = (5 + y)(2y + -5)

Reorder the terms:
-1 + -1y + 2y2 = (5 + y)(-5 + 2y)

Multiply (5 + y) * (-5 + 2y)
-1 + -1y + 2y2 = (5(-5 + 2y) + y(-5 + 2y))
-1 + -1y + 2y2 = ((-5 * 5 + 2y * 5) + y(-5 + 2y))
-1 + -1y + 2y2 = ((-25 + 10y) + y(-5 + 2y))
-1 + -1y + 2y2 = (-25 + 10y + (-5 * y + 2y * y))
-1 + -1y + 2y2 = (-25 + 10y + (-5y + 2y2))

Combine like terms: 10y + -5y = 5y
-1 + -1y + 2y2 = (-25 + 5y + 2y2)

Add '-2y2' to each side of the equation.
-1 + -1y + 2y2 + -2y2 = -25 + 5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-1 + -1y + 0 = -25 + 5y + 2y2 + -2y2
-1 + -1y = -25 + 5y + 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-1 + -1y = -25 + 5y + 0
-1 + -1y = -25 + 5y

Solving
-1 + -1y = -25 + 5y

Solving for variable 'y'.

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

Add '-5y' to each side of the equation.
-1 + -1y + -5y = -25 + 5y + -5y

Combine like terms: -1y + -5y = -6y
-1 + -6y = -25 + 5y + -5y

Combine like terms: 5y + -5y = 0
-1 + -6y = -25 + 0
-1 + -6y = -25

Add '1' to each side of the equation.
-1 + 1 + -6y = -25 + 1

Combine like terms: -1 + 1 = 0
0 + -6y = -25 + 1
-6y = -25 + 1

Combine like terms: -25 + 1 = -24
-6y = -24

Divide each side by '-6'.
y = 4

Simplifying
y = 4

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