(z-2)(z+4)=0

Solution for (z-2)(z+4)=0 equation:

Simplifying
(z + -2)(z + 4) = 0

Reorder the terms:
(-2 + z)(z + 4) = 0

Reorder the terms:
(-2 + z)(4 + z) = 0

Multiply (-2 + z) * (4 + z)
(-2(4 + z) + z(4 + z)) = 0
((4 * -2 + z * -2) + z(4 + z)) = 0
((-8 + -2z) + z(4 + z)) = 0
(-8 + -2z + (4 * z + z * z)) = 0
(-8 + -2z + (4z + z2)) = 0

Combine like terms: -2z + 4z = 2z
(-8 + 2z + z2) = 0

Solving
-8 + 2z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(2 + -1z) = 0

Subproblem 1
Set the factor '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

Move all terms containing z to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4
Subproblem 2
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
Solution
z = {-4, 2}