(2z+3)(6+z)=0

Solution for (2z+3)(6+z)=0 equation:

Simplifying
(2z + 3)(6 + z) = 0

Reorder the terms:
(3 + 2z)(6 + z) = 0

Multiply (3 + 2z) * (6 + z)
(3(6 + z) + 2z * (6 + z)) = 0
((6 * 3 + z * 3) + 2z * (6 + z)) = 0
((18 + 3z) + 2z * (6 + z)) = 0
(18 + 3z + (6 * 2z + z * 2z)) = 0
(18 + 3z + (12z + 2z2)) = 0

Combine like terms: 3z + 12z = 15z
(18 + 15z + 2z2) = 0

Solving
18 + 15z + 2z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(6 + z)' equal to zero and attempt to solve:

Simplifying
6 + z = 0

Solving
6 + z = 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 + z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + z = 0 + -6
z = 0 + -6

Combine like terms: 0 + -6 = -6
z = -6

Simplifying
z = -6
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 = {-6, -1.5}