3z(z+8)(z-3)=0

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Solution for 3z(z+8)(z-3)=0 equation: 


Simplifying
3z(z + 8)(z + -3) = 0

Reorder the terms:
3z(8 + z)(z + -3) = 0

Reorder the terms:
3z(8 + z)(-3 + z) = 0

Multiply (8 + z) * (-3 + z)
3z(8(-3 + z) + z(-3 + z)) = 0
3z((-3 * 8 + z * 8) + z(-3 + z)) = 0
3z((-24 + 8z) + z(-3 + z)) = 0
3z(-24 + 8z + (-3 * z + z * z)) = 0
3z(-24 + 8z + (-3z + z2)) = 0

Combine like terms: 8z + -3z = 5z
3z(-24 + 5z + z2) = 0
(-24 * 3z + 5z * 3z + z2 * 3z) = 0
(-72z + 15z2 + 3z3) = 0

Solving
-72z + 15z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(-24 + 5z + z2) = 0

Factor a trinomial.
3z((-8 + -1z)(3 + -1z)) = 0

Ignore the factor 3.

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 '(-8 + -1z)' equal to zero and attempt to solve:

Simplifying
-8 + -1z = 0

Solving
-8 + -1z = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1z = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1z = 0 + 8
-1z = 0 + 8

Combine like terms: 0 + 8 = 8
-1z = 8

Divide each side by '-1'.
z = -8

Simplifying
z = -8

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, -8, 3}

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