(4z+6)(3-z)=0

Solution for (4z+6)(3-z)=0 equation:

Simplifying
(4z + 6)(3 + -1z) = 0

Reorder the terms:
(6 + 4z)(3 + -1z) = 0

Multiply (6 + 4z) * (3 + -1z)
(6(3 + -1z) + 4z * (3 + -1z)) = 0
((3 * 6 + -1z * 6) + 4z * (3 + -1z)) = 0
((18 + -6z) + 4z * (3 + -1z)) = 0
(18 + -6z + (3 * 4z + -1z * 4z)) = 0
(18 + -6z + (12z + -4z2)) = 0

Combine like terms: -6z + 12z = 6z
(18 + 6z + -4z2) = 0

Solving
18 + 6z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 3z + -2z2) = 0

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

Ignore the factor 2.
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 '(3 + 2z)' equal to zero and attempt to solve:

Simplifying
3 + 2z = 0

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

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {3, -1.5}