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

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

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

Reorder the terms:
(7 + x)(x + -6) = 0

Reorder the terms:
(7 + x)(-6 + x) = 0

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

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

Solving
-42 + 1x + x2 = 0

Solving for variable 'x'.

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

Simplifying
6 + -1x = 0

Solving
6 + -1x = 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 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

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