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

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

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

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

Multiply (4 + 3z) * (6 + z)
(4(6 + z) + 3z * (6 + z)) = 0
((6 * 4 + z * 4) + 3z * (6 + z)) = 0
((24 + 4z) + 3z * (6 + z)) = 0
(24 + 4z + (6 * 3z + z * 3z)) = 0
(24 + 4z + (18z + 3z2)) = 0

Combine like terms: 4z + 18z = 22z
(24 + 22z + 3z2) = 0

Solving
24 + 22z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + z)(4 + 3z) = 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 '(4 + 3z)' equal to zero and attempt to solve:

Simplifying
4 + 3z = 0

Solving
4 + 3z = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 3z = 0 + -4
3z = 0 + -4

Combine like terms: 0 + -4 = -4
3z = -4

Divide each side by '3'.
z = -1.333333333

Simplifying
z = -1.333333333
Solution
z = {-6, -1.333333333}