(Y+4)(6y+2)=6(y+5)(y-2)

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Solution for (Y+4)(6y+2)=6(y+5)(y-2) equation: 


Simplifying
(Y + 4)(6y + 2) = 6(y + 5)(y + -2)

Reorder the terms:
(4 + Y)(6y + 2) = 6(y + 5)(y + -2)

Reorder the terms:
(4 + Y)(2 + 6y) = 6(y + 5)(y + -2)

Multiply (4 + Y) * (2 + 6y)
(4(2 + 6y) + Y(2 + 6y)) = 6(y + 5)(y + -2)
((2 * 4 + 6y * 4) + Y(2 + 6y)) = 6(y + 5)(y + -2)
((8 + 24y) + Y(2 + 6y)) = 6(y + 5)(y + -2)
(8 + 24y + (2 * Y + 6y * Y)) = 6(y + 5)(y + -2)
(8 + 24y + (2Y + 6yY)) = 6(y + 5)(y + -2)

Reorder the terms:
(8 + 2Y + 24y + 6yY) = 6(y + 5)(y + -2)
(8 + 2Y + 24y + 6yY) = 6(y + 5)(y + -2)

Reorder the terms:
8 + 2Y + 24y + 6yY = 6(5 + y)(y + -2)

Reorder the terms:
8 + 2Y + 24y + 6yY = 6(5 + y)(-2 + y)

Multiply (5 + y) * (-2 + y)
8 + 2Y + 24y + 6yY = 6(5(-2 + y) + y(-2 + y))
8 + 2Y + 24y + 6yY = 6((-2 * 5 + y * 5) + y(-2 + y))
8 + 2Y + 24y + 6yY = 6((-10 + 5y) + y(-2 + y))
8 + 2Y + 24y + 6yY = 6(-10 + 5y + (-2 * y + y * y))
8 + 2Y + 24y + 6yY = 6(-10 + 5y + (-2y + y2))

Combine like terms: 5y + -2y = 3y
8 + 2Y + 24y + 6yY = 6(-10 + 3y + y2)
8 + 2Y + 24y + 6yY = (-10 * 6 + 3y * 6 + y2 * 6)
8 + 2Y + 24y + 6yY = (-60 + 18y + 6y2)

Solving
8 + 2Y + 24y + 6yY = -60 + 18y + 6y2

Solving for variable 'Y'.

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

Add '-8' to each side of the equation.
8 + 2Y + 24y + -8 + 6yY = -60 + 18y + -8 + 6y2

Reorder the terms:
8 + -8 + 2Y + 24y + 6yY = -60 + 18y + -8 + 6y2

Combine like terms: 8 + -8 = 0
0 + 2Y + 24y + 6yY = -60 + 18y + -8 + 6y2
2Y + 24y + 6yY = -60 + 18y + -8 + 6y2

Reorder the terms:
2Y + 24y + 6yY = -60 + -8 + 18y + 6y2

Combine like terms: -60 + -8 = -68
2Y + 24y + 6yY = -68 + 18y + 6y2

Add '-24y' to each side of the equation.
2Y + 24y + -24y + 6yY = -68 + 18y + -24y + 6y2

Combine like terms: 24y + -24y = 0
2Y + 0 + 6yY = -68 + 18y + -24y + 6y2
2Y + 6yY = -68 + 18y + -24y + 6y2

Combine like terms: 18y + -24y = -6y
2Y + 6yY = -68 + -6y + 6y2

Reorder the terms:
68 + 2Y + 6y + 6yY + -6y2 = -68 + -6y + 6y2 + 68 + 6y + -6y2

Reorder the terms:
68 + 2Y + 6y + 6yY + -6y2 = -68 + 68 + -6y + 6y + 6y2 + -6y2

Combine like terms: -68 + 68 = 0
68 + 2Y + 6y + 6yY + -6y2 = 0 + -6y + 6y + 6y2 + -6y2
68 + 2Y + 6y + 6yY + -6y2 = -6y + 6y + 6y2 + -6y2

Combine like terms: -6y + 6y = 0
68 + 2Y + 6y + 6yY + -6y2 = 0 + 6y2 + -6y2
68 + 2Y + 6y + 6yY + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
68 + 2Y + 6y + 6yY + -6y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(34 + Y + 3y + 3yY + -3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(34 + Y + 3y + 3yY + -3y2)' equal to zero and attempt to solve:

Simplifying
34 + Y + 3y + 3yY + -3y2 = 0

Solving
34 + Y + 3y + 3yY + -3y2 = 0

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

Add '-34' to each side of the equation.
34 + Y + 3y + 3yY + -34 + -3y2 = 0 + -34

Reorder the terms:
34 + -34 + Y + 3y + 3yY + -3y2 = 0 + -34

Combine like terms: 34 + -34 = 0
0 + Y + 3y + 3yY + -3y2 = 0 + -34
Y + 3y + 3yY + -3y2 = 0 + -34

Combine like terms: 0 + -34 = -34
Y + 3y + 3yY + -3y2 = -34

Add '-3y' to each side of the equation.
Y + 3y + 3yY + -3y + -3y2 = -34 + -3y

Reorder the terms:
Y + 3y + -3y + 3yY + -3y2 = -34 + -3y

Combine like terms: 3y + -3y = 0
Y + 0 + 3yY + -3y2 = -34 + -3y
Y + 3yY + -3y2 = -34 + -3y

Add '3y2' to each side of the equation.
Y + 3yY + -3y2 + 3y2 = -34 + -3y + 3y2

Combine like terms: -3y2 + 3y2 = 0
Y + 3yY + 0 = -34 + -3y + 3y2
Y + 3yY = -34 + -3y + 3y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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