(6+z)(3z-2)=0

Solution for (6+z)(3z-2)=0 equation:

Simplifying
(6 + z)(3z + -2) = 0

Reorder the terms:
(6 + z)(-2 + 3z) = 0

Multiply (6 + z) * (-2 + 3z)
(6(-2 + 3z) + z(-2 + 3z)) = 0
((-2 * 6 + 3z * 6) + z(-2 + 3z)) = 0
((-12 + 18z) + z(-2 + 3z)) = 0
(-12 + 18z + (-2 * z + 3z * z)) = 0
(-12 + 18z + (-2z + 3z2)) = 0

Combine like terms: 18z + -2z = 16z
(-12 + 16z + 3z2) = 0

Solving
-12 + 16z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(2 + -3z) = 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 '(2 + -3z)' equal to zero and attempt to solve:

Simplifying
2 + -3z = 0

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

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

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

Divide each side by '-3'.
z = 0.6666666667

Simplifying
z = 0.6666666667
Solution
z = {-6, 0.6666666667}