(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 = -6x
(-7 + -6x + x2) = 0

Solving
-7 + -6x + 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}