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

Solution for (3+z)(2z-9)=0 equation:

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

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

Multiply (3 + z) * (-9 + 2z)
(3(-9 + 2z) + z(-9 + 2z)) = 0
((-9 * 3 + 2z * 3) + z(-9 + 2z)) = 0
((-27 + 6z) + z(-9 + 2z)) = 0
(-27 + 6z + (-9 * z + 2z * z)) = 0
(-27 + 6z + (-9z + 2z2)) = 0

Combine like terms: 6z + -9z = -3z
(-27 + -3z + 2z2) = 0

Solving
-27 + -3z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(9 + -2z) = 0

Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
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 = {-3, 4.5}