(y-4)(y-6)=0

Solution for (y-4)(y-6)=0 equation:

Simplifying
(y + -4)(y + -6) = 0

Reorder the terms:
(-4 + y)(y + -6) = 0

Reorder the terms:
(-4 + y)(-6 + y) = 0

Multiply (-4 + y) * (-6 + y)
(-4(-6 + y) + y(-6 + y)) = 0
((-6 * -4 + y * -4) + y(-6 + y)) = 0
((24 + -4y) + y(-6 + y)) = 0
(24 + -4y + (-6 * y + y * y)) = 0
(24 + -4y + (-6y + y2)) = 0

Combine like terms: -4y + -6y = -10y
(24 + -10y + y2) = 0

Solving
24 + -10y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(4 + -1y)(6 + -1y) = 0

Subproblem 1
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

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

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

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Subproblem 2
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {4, 6}