(7+-1x)(6+x)=0

Solution for (7+-1x)(6+x)=0 equation:

Simplifying
(7 + -1x)(6 + x) = 0

Multiply (7 + -1x) * (6 + x)
(7(6 + x) + -1x * (6 + x)) = 0
((6 * 7 + x * 7) + -1x * (6 + x)) = 0
((42 + 7x) + -1x * (6 + x)) = 0
(42 + 7x + (6 * -1x + x * -1x)) = 0
(42 + 7x + (-6x + -1x2)) = 0

Combine like terms: 7x + -6x = 1x
(42 + 1x + -1x2) = 0

Solving
42 + 1x + -1x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(7 + -1x)(6 + x) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 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 + x = 0 + -6

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

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

Simplifying
x = -6
Solution
x = {7, -6}