(z-6)(z-7)=0

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

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

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

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

Multiply (-6 + z) * (-7 + z)
(-6(-7 + z) + z(-7 + z)) = 0
((-7 * -6 + z * -6) + z(-7 + z)) = 0
((42 + -6z) + z(-7 + z)) = 0
(42 + -6z + (-7 * z + z * z)) = 0
(42 + -6z + (-7z + z2)) = 0

Combine like terms: -6z + -7z = -13z
(42 + -13z + z2) = 0

Solving
42 + -13z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

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

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

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

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

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

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

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

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

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

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

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