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

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


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

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

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

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

Combine like terms: 1y + -3y = -2y
(-1 + -2y + 3y2) = (y + 5)(2y + -5)

Reorder the terms:
-1 + -2y + 3y2 = (5 + y)(2y + -5)

Reorder the terms:
-1 + -2y + 3y2 = (5 + y)(-5 + 2y)

Multiply (5 + y) * (-5 + 2y)
-1 + -2y + 3y2 = (5(-5 + 2y) + y(-5 + 2y))
-1 + -2y + 3y2 = ((-5 * 5 + 2y * 5) + y(-5 + 2y))
-1 + -2y + 3y2 = ((-25 + 10y) + y(-5 + 2y))
-1 + -2y + 3y2 = (-25 + 10y + (-5 * y + 2y * y))
-1 + -2y + 3y2 = (-25 + 10y + (-5y + 2y2))

Combine like terms: 10y + -5y = 5y
-1 + -2y + 3y2 = (-25 + 5y + 2y2)

Solving
-1 + -2y + 3y2 = -25 + 5y + 2y2

Solving for variable 'y'.

Reorder the terms:
-1 + 25 + -2y + -5y + 3y2 + -2y2 = -25 + 5y + 2y2 + 25 + -5y + -2y2

Combine like terms: -1 + 25 = 24
24 + -2y + -5y + 3y2 + -2y2 = -25 + 5y + 2y2 + 25 + -5y + -2y2

Combine like terms: -2y + -5y = -7y
24 + -7y + 3y2 + -2y2 = -25 + 5y + 2y2 + 25 + -5y + -2y2

Combine like terms: 3y2 + -2y2 = 1y2
24 + -7y + 1y2 = -25 + 5y + 2y2 + 25 + -5y + -2y2

Reorder the terms:
24 + -7y + 1y2 = -25 + 25 + 5y + -5y + 2y2 + -2y2

Combine like terms: -25 + 25 = 0
24 + -7y + 1y2 = 0 + 5y + -5y + 2y2 + -2y2
24 + -7y + 1y2 = 5y + -5y + 2y2 + -2y2

Combine like terms: 5y + -5y = 0
24 + -7y + 1y2 = 0 + 2y2 + -2y2
24 + -7y + 1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
24 + -7y + 1y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-24' to each side of the equation.
24 + -7y + -24 + y2 = 0 + -24

Reorder the terms:
24 + -24 + -7y + y2 = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -7y + y2 = 0 + -24
-7y + y2 = 0 + -24

Combine like terms: 0 + -24 = -24
-7y + y2 = -24

The y term is -7y.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7y + 12.25 + y2 = -24 + 12.25

Reorder the terms:
12.25 + -7y + y2 = -24 + 12.25

Combine like terms: -24 + 12.25 = -11.75
12.25 + -7y + y2 = -11.75

Factor a perfect square on the left side:
(y + -3.5)(y + -3.5) = -11.75

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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