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

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

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

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

Multiply (9 + z) * (3 + 4z)
(9(3 + 4z) + z(3 + 4z)) = 0
((3 * 9 + 4z * 9) + z(3 + 4z)) = 0
((27 + 36z) + z(3 + 4z)) = 0
(27 + 36z + (3 * z + 4z * z)) = 0
(27 + 36z + (3z + 4z2)) = 0

Combine like terms: 36z + 3z = 39z
(27 + 39z + 4z2) = 0

Solving
27 + 39z + 4z2 = 0

Solving for variable 'z'.

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

Subproblem 1
Set the factor '(9 + z)' equal to zero and attempt to solve:

Simplifying
9 + z = 0

Solving
9 + z = 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 + z = 0 + -9

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

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

Simplifying
z = -9
Subproblem 2
Set the factor '(3 + 4z)' equal to zero and attempt to solve:

Simplifying
3 + 4z = 0

Solving
3 + 4z = 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 + 4z = 0 + -3

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

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

Divide each side by '4'.
z = -0.75

Simplifying
z = -0.75
Solution
z = {-9, -0.75}