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

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

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

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

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

Combine like terms: -4z + 18z = 14z
(-24 + 14z + 3z2) = 0

Solving
-24 + 14z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(4 + -3z) = 0

Subproblem 1
Set the factor '(-6 + -1z)' equal to zero and attempt to solve:

Simplifying
-6 + -1z = 0

Solving
-6 + -1z = 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 + -1z = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1z = 0 + 6
-1z = 0 + 6

Combine like terms: 0 + 6 = 6
-1z = 6

Divide each side by '-1'.
z = -6

Simplifying
z = -6
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 = {-6, 1.333333333}