2(z-5)(-z-3)=0

Solution for 2(z-5)(-z-3)=0 equation:

Simplifying
2(z + -5)(-1z + -3) = 0

Reorder the terms:
2(-5 + z)(-1z + -3) = 0

Reorder the terms:
2(-5 + z)(-3 + -1z) = 0

Multiply (-5 + z) * (-3 + -1z)
2(-5(-3 + -1z) + z(-3 + -1z)) = 0
2((-3 * -5 + -1z * -5) + z(-3 + -1z)) = 0
2((15 + 5z) + z(-3 + -1z)) = 0
2(15 + 5z + (-3 * z + -1z * z)) = 0
2(15 + 5z + (-3z + -1z2)) = 0

Combine like terms: 5z + -3z = 2z
2(15 + 2z + -1z2) = 0
(15 * 2 + 2z * 2 + -1z2 * 2) = 0
(30 + 4z + -2z2) = 0

Solving
30 + 4z + -2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 2z + -1z2) = 0

Factor a trinomial.
2((5 + -1z)(3 + z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Subproblem 2
Set the factor '(3 + z)' equal to zero and attempt to solve:

Simplifying
3 + z = 0

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

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

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

Simplifying
z = -3
Solution
z = {5, -3}