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

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

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

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

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

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

Solving
18 + 18z + 4z2 = 0

Solving for variable 'z'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

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

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

Combine like terms: 0 + -3 = -3
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}