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

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

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

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

Multiply (-6 + 4z) * (3 + z)
(-6(3 + z) + 4z * (3 + z)) = 0
((3 * -6 + z * -6) + 4z * (3 + z)) = 0
((-18 + -6z) + 4z * (3 + z)) = 0
(-18 + -6z + (3 * 4z + z * 4z)) = 0
(-18 + -6z + (12z + 4z2)) = 0

Combine like terms: -6z + 12z = 6z
(-18 + 6z + 4z2) = 0

Solving
-18 + 6z + 4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 3z + 2z2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1z)' equal to zero and attempt to solve:

Simplifying
-3 + -1z = 0

Solving
-3 + -1z = 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 + -1z = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1z = 0 + 3
-1z = 0 + 3

Combine like terms: 0 + 3 = 3
-1z = 3

Divide each side by '-1'.
z = -3

Simplifying
z = -3
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 = {-3, 1.5}