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

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

Simplifying
(y + -6)(4 + -1y) = 0

Reorder the terms:
(-6 + y)(4 + -1y) = 0

Multiply (-6 + y) * (4 + -1y)
(-6(4 + -1y) + y(4 + -1y)) = 0
((4 * -6 + -1y * -6) + y(4 + -1y)) = 0
((-24 + 6y) + y(4 + -1y)) = 0
(-24 + 6y + (4 * y + -1y * y)) = 0
(-24 + 6y + (4y + -1y2)) = 0

Combine like terms: 6y + 4y = 10y
(-24 + 10y + -1y2) = 0

Solving
-24 + 10y + -1y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-6 + y = 0

Solving
-6 + y = 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 + y = 0 + 6

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

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

Simplifying
y = 6
Subproblem 2
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
Solution
y = {6, 4}