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

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

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

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

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

Combine like terms: 12z + -6z = 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}