(a-6)(a-7)=0

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

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

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

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

Multiply (-6 + a) * (-7 + a)
(-6(-7 + a) + a(-7 + a)) = 0
((-7 * -6 + a * -6) + a(-7 + a)) = 0
((42 + -6a) + a(-7 + a)) = 0
(42 + -6a + (-7 * a + a * a)) = 0
(42 + -6a + (-7a + a2)) = 0

Combine like terms: -6a + -7a = -13a
(42 + -13a + a2) = 0

Solving
42 + -13a + a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(6 + -1a)' equal to zero and attempt to solve:

Simplifying
6 + -1a = 0

Solving
6 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-6' to each side of the equation.
6 + -6 + -1a = 0 + -6

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

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

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

Simplifying
a = 6
Subproblem 2
Set the factor '(7 + -1a)' equal to zero and attempt to solve:

Simplifying
7 + -1a = 0

Solving
7 + -1a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-7' to each side of the equation.
7 + -7 + -1a = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1a = 0 + -7
-1a = 0 + -7

Combine like terms: 0 + -7 = -7
-1a = -7

Divide each side by '-1'.
a = 7

Simplifying
a = 7
Solution
a = {6, 7}