(3z-7)(6+z)=0

Solution for (3z-7)(6+z)=0 equation:

Simplifying
(3z + -7)(6 + z) = 0

Reorder the terms:
(-7 + 3z)(6 + z) = 0

Multiply (-7 + 3z) * (6 + z)
(-7(6 + z) + 3z * (6 + z)) = 0
((6 * -7 + z * -7) + 3z * (6 + z)) = 0
((-42 + -7z) + 3z * (6 + z)) = 0
(-42 + -7z + (6 * 3z + z * 3z)) = 0
(-42 + -7z + (18z + 3z2)) = 0

Combine like terms: -7z + 18z = 11z
(-42 + 11z + 3z2) = 0

Solving
-42 + 11z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(7 + -3z) = 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 + -3z)' equal to zero and attempt to solve:

Simplifying
7 + -3z = 0

Solving
7 + -3z = 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 + -3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -3z = 0 + -7
-3z = 0 + -7

Combine like terms: 0 + -7 = -7
-3z = -7

Divide each side by '-3'.
z = 2.333333333

Simplifying
z = 2.333333333
Solution
z = {-6, 2.333333333}