(2z+9)(6-z)=0

Solution for (2z+9)(6-z)=0 equation:

Simplifying
(2z + 9)(6 + -1z) = 0

Reorder the terms:
(9 + 2z)(6 + -1z) = 0

Multiply (9 + 2z) * (6 + -1z)
(9(6 + -1z) + 2z * (6 + -1z)) = 0
((6 * 9 + -1z * 9) + 2z * (6 + -1z)) = 0
((54 + -9z) + 2z * (6 + -1z)) = 0
(54 + -9z + (6 * 2z + -1z * 2z)) = 0
(54 + -9z + (12z + -2z2)) = 0

Combine like terms: -9z + 12z = 3z
(54 + 3z + -2z2) = 0

Solving
54 + 3z + -2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(9 + 2z) = 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 '(9 + 2z)' equal to zero and attempt to solve:

Simplifying
9 + 2z = 0

Solving
9 + 2z = 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 + 2z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2z = 0 + -9
2z = 0 + -9

Combine like terms: 0 + -9 = -9
2z = -9

Divide each side by '2'.
z = -4.5

Simplifying
z = -4.5
Solution
z = {6, -4.5}