(4z-9)(3+z)=0

Solution for (4z-9)(3+z)=0 equation:

Simplifying
(4z + -9)(3 + z) = 0

Reorder the terms:
(-9 + 4z)(3 + z) = 0

Multiply (-9 + 4z) * (3 + z)
(-9(3 + z) + 4z * (3 + z)) = 0
((3 * -9 + z * -9) + 4z * (3 + z)) = 0
((-27 + -9z) + 4z * (3 + z)) = 0
(-27 + -9z + (3 * 4z + z * 4z)) = 0
(-27 + -9z + (12z + 4z2)) = 0

Combine like terms: -9z + 12z = 3z
(-27 + 3z + 4z2) = 0

Solving
-27 + 3z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(9 + -4z) = 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 + -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 = {-3, 2.25}