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

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

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

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

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

Combine like terms: 9z + 4z = 13z
(12 + 13z + 3z2) = 0

Solving
12 + 13z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(4 + 3z) = 0

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 '(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 = {-3, -1.333333333}