(x-10)(x-1)=0

Solution for (x-10)(x-1)=0 equation:

Simplifying
(x + -10)(x + -1) = 0

Reorder the terms:
(-10 + x)(x + -1) = 0

Reorder the terms:
(-10 + x)(-1 + x) = 0

Multiply (-10 + x) * (-1 + x)
(-10(-1 + x) + x(-1 + x)) = 0
((-1 * -10 + x * -10) + x(-1 + x)) = 0
((10 + -10x) + x(-1 + x)) = 0
(10 + -10x + (-1 * x + x * x)) = 0
(10 + -10x + (-1x + x2)) = 0

Combine like terms: -10x + -1x = -11x
(10 + -11x + x2) = 0

Solving
10 + -11x + x2 = 0

Solving for variable 'x'.

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

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

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

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

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

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

Simplifying
x = 1
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 = {1, 10}