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

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

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

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

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

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

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

Solving
42 + -13z + z2 = 6

Solving for variable 'z'.

Reorder the terms:
42 + -6 + -13z + z2 = 6 + -6

Combine like terms: 42 + -6 = 36
36 + -13z + z2 = 6 + -6

Combine like terms: 6 + -6 = 0
36 + -13z + z2 = 0

Factor a trinomial.
(4 + -1z)(9 + -1z) = 0

Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Subproblem 2
Set the factor '(9 + -1z)' equal to zero and attempt to solve:

Simplifying
9 + -1z = 0

Solving
9 + -1z = 0

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

Add '-9' to each side of the equation.
9 + -9 + -1z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -1z = 0 + -9
-1z = 0 + -9

Combine like terms: 0 + -9 = -9
-1z = -9

Divide each side by '-1'.
z = 9

Simplifying
z = 9
Solution
z = {4, 9}