(6-z)(4z+9)=0

Solution for (6-z)(4z+9)=0 equation:

Simplifying
(6 + -1z)(4z + 9) = 0

Reorder the terms:
(6 + -1z)(9 + 4z) = 0

Multiply (6 + -1z) * (9 + 4z)
(6(9 + 4z) + -1z * (9 + 4z)) = 0
((9 * 6 + 4z * 6) + -1z * (9 + 4z)) = 0
((54 + 24z) + -1z * (9 + 4z)) = 0
(54 + 24z + (9 * -1z + 4z * -1z)) = 0
(54 + 24z + (-9z + -4z2)) = 0

Combine like terms: 24z + -9z = 15z
(54 + 15z + -4z2) = 0

Solving
54 + 15z + -4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + -1z)(9 + 4z) = 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 + 4z)' equal to zero and attempt to solve:

Simplifying
9 + 4z = 0

Solving
9 + 4z = 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 + 4z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4z = 0 + -9
4z = 0 + -9

Combine like terms: 0 + -9 = -9
4z = -9

Divide each side by '4'.
z = -2.25

Simplifying
z = -2.25
Solution
z = {6, -2.25}