(3z+7)(3+z)=0

Solution for (3z+7)(3+z)=0 equation:

Simplifying
(3z + 7)(3 + z) = 0

Reorder the terms:
(7 + 3z)(3 + z) = 0

Multiply (7 + 3z) * (3 + z)
(7(3 + z) + 3z * (3 + z)) = 0
((3 * 7 + z * 7) + 3z * (3 + z)) = 0
((21 + 7z) + 3z * (3 + z)) = 0
(21 + 7z + (3 * 3z + z * 3z)) = 0
(21 + 7z + (9z + 3z2)) = 0

Combine like terms: 7z + 9z = 16z
(21 + 16z + 3z2) = 0

Solving
21 + 16z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(7 + 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 '(7 + 3z)' equal to zero and attempt to solve:

Simplifying
7 + 3z = 0

Solving
7 + 3z = 0

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

Add '-7' to each side of the equation.
7 + -7 + 3z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 3z = 0 + -7
3z = 0 + -7

Combine like terms: 0 + -7 = -7
3z = -7

Divide each side by '3'.
z = -2.333333333

Simplifying
z = -2.333333333
Solution
z = {-3, -2.333333333}