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

Solution for 4(z+3)(-z+5)=0 equation:

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

Reorder the terms:
4(3 + z)(-1z + 5) = 0

Reorder the terms:
4(3 + z)(5 + -1z) = 0

Multiply (3 + z) * (5 + -1z)
4(3(5 + -1z) + z(5 + -1z)) = 0
4((5 * 3 + -1z * 3) + z(5 + -1z)) = 0
4((15 + -3z) + z(5 + -1z)) = 0
4(15 + -3z + (5 * z + -1z * z)) = 0
4(15 + -3z + (5z + -1z2)) = 0

Combine like terms: -3z + 5z = 2z
4(15 + 2z + -1z2) = 0
(15 * 4 + 2z * 4 + -1z2 * 4) = 0
(60 + 8z + -4z2) = 0

Solving
60 + 8z + -4z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4'.
4(15 + 2z + -1z2) = 0

Factor a trinomial.
4((5 + -1z)(3 + z)) = 0

Ignore the factor 4.
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}