y(5-y)=17-(3-y)

Solution for y(5-y)=17-(3-y) equation:

Simplifying
y(5 + -1y) = 17 + -1(3 + -1y)
(5 * y + -1y * y) = 17 + -1(3 + -1y)
(5y + -1y2) = 17 + -1(3 + -1y)
5y + -1y2 = 17 + (3 * -1 + -1y * -1)
5y + -1y2 = 17 + (-3 + 1y)

Combine like terms: 17 + -3 = 14
5y + -1y2 = 14 + 1y

Solving
5y + -1y2 = 14 + 1y

Solving for variable 'y'.

Reorder the terms:
-14 + 5y + -1y + -1y2 = 14 + 1y + -14 + -1y

Combine like terms: 5y + -1y = 4y
-14 + 4y + -1y2 = 14 + 1y + -14 + -1y

Reorder the terms:
-14 + 4y + -1y2 = 14 + -14 + 1y + -1y

Combine like terms: 14 + -14 = 0
-14 + 4y + -1y2 = 0 + 1y + -1y
-14 + 4y + -1y2 = 1y + -1y

Combine like terms: 1y + -1y = 0
-14 + 4y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
14 + -4y + y2 = 0

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -4y + -14 + y2 = 0 + -14

Reorder the terms:
14 + -14 + -4y + y2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -4y + y2 = 0 + -14
-4y + y2 = 0 + -14

Combine like terms: 0 + -14 = -14
-4y + y2 = -14

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = -14 + 4

Reorder the terms:
4 + -4y + y2 = -14 + 4

Combine like terms: -14 + 4 = -10
4 + -4y + y2 = -10

Factor a perfect square on the left side:
(y + -2)(y + -2) = -10

Can't calculate square root of the right side.

The solution to this equation could not be determined.