(x-7)(x-1)=0

Solution for (x-7)(x-1)=0 equation:

Simplifying
(x + -7)(x + -1) = 0

Reorder the terms:
(-7 + x)(x + -1) = 0

Reorder the terms:
(-7 + x)(-1 + x) = 0

Multiply (-7 + x) * (-1 + x)
(-7(-1 + x) + x(-1 + x)) = 0
((-1 * -7 + x * -7) + x(-1 + x)) = 0
((7 + -7x) + x(-1 + x)) = 0
(7 + -7x + (-1 * x + x * x)) = 0
(7 + -7x + (-1x + x2)) = 0

Combine like terms: -7x + -1x = -8x
(7 + -8x + x2) = 0

Solving
7 + -8x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(7 + -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 '(7 + -1x)' equal to zero and attempt to solve:

Simplifying
7 + -1x = 0

Solving
7 + -1x = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1x = 0 + -7
-1x = 0 + -7

Combine like terms: 0 + -7 = -7
-1x = -7

Divide each side by '-1'.
x = 7

Simplifying
x = 7
Solution
x = {1, 7}