(4z-1)(6+z)=0

Solution for (4z-1)(6+z)=0 equation:

Simplifying
(4z + -1)(6 + z) = 0

Reorder the terms:
(-1 + 4z)(6 + z) = 0

Multiply (-1 + 4z) * (6 + z)
(-1(6 + z) + 4z * (6 + z)) = 0
((6 * -1 + z * -1) + 4z * (6 + z)) = 0
((-6 + -1z) + 4z * (6 + z)) = 0
(-6 + -1z + (6 * 4z + z * 4z)) = 0
(-6 + -1z + (24z + 4z2)) = 0

Combine like terms: -1z + 24z = 23z
(-6 + 23z + 4z2) = 0

Solving
-6 + 23z + 4z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(1 + -4z) = 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 '(1 + -4z)' equal to zero and attempt to solve:

Simplifying
1 + -4z = 0

Solving
1 + -4z = 0

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

Add '-1' to each side of the equation.
1 + -1 + -4z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4z = 0 + -1
-4z = 0 + -1

Combine like terms: 0 + -1 = -1
-4z = -1

Divide each side by '-4'.
z = 0.25

Simplifying
z = 0.25
Solution
z = {-6, 0.25}