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

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

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

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

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

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

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

Solving
0 = 7 + -8x + x2

Solving for variable 'x'.

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

Reorder the terms:
-7 + 8x + -1x2 = 7 + -7 + -8x + 8x + x2 + -1x2

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

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

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

Factor a trinomial.
(-7 + x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-7 + x)' equal to zero and attempt to solve:

Simplifying
-7 + x = 0

Solving
-7 + x = 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 + x = 0 + 7

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

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

Simplifying
x = 7
Subproblem 2
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
Solution
x = {7, 1}