(4z+6)(2-z)=0

Solution for (4z+6)(2-z)=0 equation:

Simplifying
(4z + 6)(2 + -1z) = 0

Reorder the terms:
(6 + 4z)(2 + -1z) = 0

Multiply (6 + 4z) * (2 + -1z)
(6(2 + -1z) + 4z * (2 + -1z)) = 0
((2 * 6 + -1z * 6) + 4z * (2 + -1z)) = 0
((12 + -6z) + 4z * (2 + -1z)) = 0
(12 + -6z + (2 * 4z + -1z * 4z)) = 0
(12 + -6z + (8z + -4z2)) = 0

Combine like terms: -6z + 8z = 2z
(12 + 2z + -4z2) = 0

Solving
12 + 2z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(6 + z + -2z2) = 0

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

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
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 = {2, -1.5}