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

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

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

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

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

Combine like terms: 12z + -9z = 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}