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

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

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

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

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

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

Combine like terms: -6x + -7x = -13x
(42 + -13x + x2) = 0

Solving
42 + -13x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + -1x)(7 + -1x) = 0

Subproblem 1
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
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 = {6, 7}