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

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

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

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

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

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

Combine like terms: -3z + 5z = 2z
2z(-15 + 2z + z2) = 0
(-15 * 2z + 2z * 2z + z2 * 2z) = 0
(-30z + 4z2 + 2z3) = 0

Solving
-30z + 4z2 + 2z3 = 0

Solving for variable 'z'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Simplifying
z = 0
Subproblem 2
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 3
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 = {0, -5, 3}