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

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

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

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

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

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

Combine like terms: -6z + 3z = -3z
(-18 + -3z + z2) = 0

Solving
-18 + -3z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-3 + -1z)(6 + -1z) = 0

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 '(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
Solution
z = {-3, 6}