3z(z+8)(z+5)=0

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Solution for 3z(z+8)(z+5)=0 equation: 


Simplifying
3z(z + 8)(z + 5) = 0

Reorder the terms:
3z(8 + z)(z + 5) = 0

Reorder the terms:
3z(8 + z)(5 + z) = 0

Multiply (8 + z) * (5 + z)
3z(8(5 + z) + z(5 + z)) = 0
3z((5 * 8 + z * 8) + z(5 + z)) = 0
3z((40 + 8z) + z(5 + z)) = 0
3z(40 + 8z + (5 * z + z * z)) = 0
3z(40 + 8z + (5z + z2)) = 0

Combine like terms: 8z + 5z = 13z
3z(40 + 13z + z2) = 0
(40 * 3z + 13z * 3z + z2 * 3z) = 0
(120z + 39z2 + 3z3) = 0

Solving
120z + 39z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '3z'.
3z(40 + 13z + z2) = 0

Factor a trinomial.
3z((8 + z)(5 + z)) = 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 + z)' equal to zero and attempt to solve:

Simplifying
8 + z = 0

Solving
8 + z = 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 + z = 0 + -8

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

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

Simplifying
z = -8

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

Simplifying
5 + z = 0

Solving
5 + z = 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 + z = 0 + -5

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

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

Simplifying
z = -5
Solution
z = {0, -8, -5}

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