(y-10)(y-5)=

Solution for (y-10)(y-5)= equation:

Simplifying
(y + -10)(y + -5) = 0

Reorder the terms:
(-10 + y)(y + -5) = 0

Reorder the terms:
(-10 + y)(-5 + y) = 0

Multiply (-10 + y) * (-5 + y)
(-10(-5 + y) + y(-5 + y)) = 0
((-5 * -10 + y * -10) + y(-5 + y)) = 0
((50 + -10y) + y(-5 + y)) = 0
(50 + -10y + (-5 * y + y * y)) = 0
(50 + -10y + (-5y + y2)) = 0

Combine like terms: -10y + -5y = -15y
(50 + -15y + y2) = 0

Solving
50 + -15y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(10 + -1y) = 0

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Subproblem 2
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Solution
y = {5, 10}