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

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

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

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

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

Combine like terms: -3z + 12z = 9z
(-18 + 9z + 2z2) = 0

Solving
-18 + 9z + 2z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-6 + -1z)(3 + -2z) = 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 '(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 = {-6, 1.5}