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

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

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

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

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

Combine like terms: 24z + 3z = 27z
(18 + 27z + 4z2) = 0

Solving
18 + 27z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(6 + z)(3 + 4z) = 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 '(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 = {-6, -0.75}