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

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

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

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

Multiply (4 + -1z) * (6 + 4z)
(4(6 + 4z) + -1z * (6 + 4z)) = 0
((6 * 4 + 4z * 4) + -1z * (6 + 4z)) = 0
((24 + 16z) + -1z * (6 + 4z)) = 0
(24 + 16z + (6 * -1z + 4z * -1z)) = 0
(24 + 16z + (-6z + -4z2)) = 0

Combine like terms: 16z + -6z = 10z
(24 + 10z + -4z2) = 0

Solving
24 + 10z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 5z + -2z2) = 0

Factor a trinomial.
2((4 + -1z)(3 + 2z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 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 + -1z = 0 + -4

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

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

Divide each side by '-1'.
z = 4

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

Simplifying
3 + 2z = 0

Solving
3 + 2z = 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 + 2z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2z = 0 + -3
2z = 0 + -3

Combine like terms: 0 + -3 = -3
2z = -3

Divide each side by '2'.
z = -1.5

Simplifying
z = -1.5
Solution
z = {4, -1.5}