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

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

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

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

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

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

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

Solving
-7 + 6x + x2 = 0

Solving for variable 'x'.

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

Subproblem 1
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
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}