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

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

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

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

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

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

Combine like terms: -3z + 2z = -1z
(-6 + -1z + z2) = 0

Solving
-6 + -1z + z2 = 0

Solving for variable 'z'.

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

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

Simplifying
-2 + -1z = 0

Solving
-2 + -1z = 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 + -1z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1z = 0 + 2
-1z = 0 + 2

Combine like terms: 0 + 2 = 2
-1z = 2

Divide each side by '-1'.
z = -2

Simplifying
z = -2
Subproblem 2
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
Solution
z = {-2, 3}