=(y-5)(y-3)

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

Simplifying
0 = (y + -5)(y + -3)

Reorder the terms:
0 = (-5 + y)(y + -3)

Reorder the terms:
0 = (-5 + y)(-3 + y)

Multiply (-5 + y) * (-3 + y)
0 = (-5(-3 + y) + y(-3 + y))
0 = ((-3 * -5 + y * -5) + y(-3 + y))
0 = ((15 + -5y) + y(-3 + y))
0 = (15 + -5y + (-3 * y + y * y))
0 = (15 + -5y + (-3y + y2))

Combine like terms: -5y + -3y = -8y
0 = (15 + -8y + y2)

Solving
0 = 15 + -8y + y2

Solving for variable 'y'.

Combine like terms: 0 + -15 = -15
-15 + 8y + -1y2 = 15 + -8y + y2 + -15 + 8y + -1y2

Reorder the terms:
-15 + 8y + -1y2 = 15 + -15 + -8y + 8y + y2 + -1y2

Combine like terms: 15 + -15 = 0
-15 + 8y + -1y2 = 0 + -8y + 8y + y2 + -1y2
-15 + 8y + -1y2 = -8y + 8y + y2 + -1y2

Combine like terms: -8y + 8y = 0
-15 + 8y + -1y2 = 0 + y2 + -1y2
-15 + 8y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-15 + 8y + -1y2 = 0

Factor a trinomial.
(-5 + y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-5 + y)' equal to zero and attempt to solve:

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

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

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {5, 3}