(y-5)(y-1)-y*y=-13

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Solution for (y-5)(y-1)-y*y=-13 equation: 


Simplifying
(y + -5)(y + -1) + -1y * y = -13

Reorder the terms:
(-5 + y)(y + -1) + -1y * y = -13

Reorder the terms:
(-5 + y)(-1 + y) + -1y * y = -13

Multiply (-5 + y) * (-1 + y)
(-5(-1 + y) + y(-1 + y)) + -1y * y = -13
((-1 * -5 + y * -5) + y(-1 + y)) + -1y * y = -13
((5 + -5y) + y(-1 + y)) + -1y * y = -13
(5 + -5y + (-1 * y + y * y)) + -1y * y = -13
(5 + -5y + (-1y + y2)) + -1y * y = -13

Combine like terms: -5y + -1y = -6y
(5 + -6y + y2) + -1y * y = -13

Multiply y * y
5 + -6y + y2 + -1y2 = -13

Combine like terms: y2 + -1y2 = 0
5 + -6y + 0 = -13
5 + -6y = -13

Solving
5 + -6y = -13

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + -6y = -13 + -5

Combine like terms: 5 + -5 = 0
0 + -6y = -13 + -5
-6y = -13 + -5

Combine like terms: -13 + -5 = -18
-6y = -18

Divide each side by '-6'.
y = 3

Simplifying
y = 3

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