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

Solution for -5(z-3)(-z+1)=0 equation:

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

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

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

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

Combine like terms: 3z + 1z = 4z
-5(-3 + 4z + -1z2) = 0
(-3 * -5 + 4z * -5 + -1z2 * -5) = 0
(15 + -20z + 5z2) = 0

Solving
15 + -20z + 5z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(3 + -4z + z2) = 0

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

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

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
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 = {1, 3}