(x-1)(x-6)=0

Solution for (x-1)(x-6)=0 equation:

Simplifying
(x + -1)(x + -6) = 0

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

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

Multiply (-1 + x) * (-6 + x)
(-1(-6 + x) + x(-6 + x)) = 0
((-6 * -1 + x * -1) + x(-6 + x)) = 0
((6 + -1x) + x(-6 + x)) = 0
(6 + -1x + (-6 * x + x * x)) = 0
(6 + -1x + (-6x + x2)) = 0

Combine like terms: -1x + -6x = -7x
(6 + -7x + x2) = 0

Solving
6 + -7x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(6 + -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 '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

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

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

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

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

Simplifying
x = 6
Solution
x = {1, 6}