(3+z)(4z+9)=0

Solution for (3+z)(4z+9)=0 equation:

Simplifying
(3 + z)(4z + 9) = 0

Reorder the terms:
(3 + z)(9 + 4z) = 0

Multiply (3 + z) * (9 + 4z)
(3(9 + 4z) + z(9 + 4z)) = 0
((9 * 3 + 4z * 3) + z(9 + 4z)) = 0
((27 + 12z) + z(9 + 4z)) = 0
(27 + 12z + (9 * z + 4z * z)) = 0
(27 + 12z + (9z + 4z2)) = 0

Combine like terms: 12z + 9z = 21z
(27 + 21z + 4z2) = 0

Solving
27 + 21z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + z)(9 + 4z) = 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 '(9 + 4z)' equal to zero and attempt to solve:

Simplifying
9 + 4z = 0

Solving
9 + 4z = 0

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

Add '-9' to each side of the equation.
9 + -9 + 4z = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 4z = 0 + -9
4z = 0 + -9

Combine like terms: 0 + -9 = -9
4z = -9

Divide each side by '4'.
z = -2.25

Simplifying
z = -2.25
Solution
z = {-3, -2.25}