Y^2-y+7=(y-1)(y-5)

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Solution for Y^2-y+7=(y-1)(y-5) equation:


Simplifying
Y2 + -1y + 7 = (y + -1)(y + -5)

Reorder the terms:
7 + Y2 + -1y = (y + -1)(y + -5)

Reorder the terms:
7 + Y2 + -1y = (-1 + y)(y + -5)

Reorder the terms:
7 + Y2 + -1y = (-1 + y)(-5 + y)

Multiply (-1 + y) * (-5 + y)
7 + Y2 + -1y = (-1(-5 + y) + y(-5 + y))
7 + Y2 + -1y = ((-5 * -1 + y * -1) + y(-5 + y))
7 + Y2 + -1y = ((5 + -1y) + y(-5 + y))
7 + Y2 + -1y = (5 + -1y + (-5 * y + y * y))
7 + Y2 + -1y = (5 + -1y + (-5y + y2))

Combine like terms: -1y + -5y = -6y
7 + Y2 + -1y = (5 + -6y + y2)

Solving
7 + Y2 + -1y = 5 + -6y + y2

Solving for variable 'Y'.

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

Add '-7' to each side of the equation.
7 + Y2 + -7 + -1y = 5 + -6y + -7 + y2

Reorder the terms:
7 + -7 + Y2 + -1y = 5 + -6y + -7 + y2

Combine like terms: 7 + -7 = 0
0 + Y2 + -1y = 5 + -6y + -7 + y2
Y2 + -1y = 5 + -6y + -7 + y2

Reorder the terms:
Y2 + -1y = 5 + -7 + -6y + y2

Combine like terms: 5 + -7 = -2
Y2 + -1y = -2 + -6y + y2

Add 'y' to each side of the equation.
Y2 + -1y + y = -2 + -6y + y + y2

Combine like terms: -1y + y = 0
Y2 + 0 = -2 + -6y + y + y2
Y2 = -2 + -6y + y + y2

Combine like terms: -6y + y = -5y
Y2 = -2 + -5y + y2

Simplifying
Y2 = -2 + -5y + y2

Reorder the terms:
2 + Y2 + 5y + -1y2 = -2 + -5y + y2 + 2 + 5y + -1y2

Reorder the terms:
2 + Y2 + 5y + -1y2 = -2 + 2 + -5y + 5y + y2 + -1y2

Combine like terms: -2 + 2 = 0
2 + Y2 + 5y + -1y2 = 0 + -5y + 5y + y2 + -1y2
2 + Y2 + 5y + -1y2 = -5y + 5y + y2 + -1y2

Combine like terms: -5y + 5y = 0
2 + Y2 + 5y + -1y2 = 0 + y2 + -1y2
2 + Y2 + 5y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
2 + Y2 + 5y + -1y2 = 0

The solution to this equation could not be determined.

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