(x-10)(x-5)=0

Solution for (x-10)(x-5)=0 equation:

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

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

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

Multiply (-10 + x) * (-5 + x)
(-10(-5 + x) + x(-5 + x)) = 0
((-5 * -10 + x * -10) + x(-5 + x)) = 0
((50 + -10x) + x(-5 + x)) = 0
(50 + -10x + (-5 * x + x * x)) = 0
(50 + -10x + (-5x + x2)) = 0

Combine like terms: -10x + -5x = -15x
(50 + -15x + x2) = 0

Solving
50 + -15x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

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

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

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

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

Simplifying
10 + -1x = 0

Solving
10 + -1x = 0

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

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

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

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

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

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