z(5z-8)(z+4)=0

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Solution for z(5z-8)(z+4)=0 equation: 


Simplifying
z(5z + -8)(z + 4) = 0

Reorder the terms:
z(-8 + 5z)(z + 4) = 0

Reorder the terms:
z(-8 + 5z)(4 + z) = 0

Multiply (-8 + 5z) * (4 + z)
z(-8(4 + z) + 5z * (4 + z)) = 0
z((4 * -8 + z * -8) + 5z * (4 + z)) = 0
z((-32 + -8z) + 5z * (4 + z)) = 0
z(-32 + -8z + (4 * 5z + z * 5z)) = 0
z(-32 + -8z + (20z + 5z2)) = 0

Combine like terms: -8z + 20z = 12z
z(-32 + 12z + 5z2) = 0
(-32 * z + 12z * z + 5z2 * z) = 0
(-32z + 12z2 + 5z3) = 0

Solving
-32z + 12z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-32 + 12z + 5z2) = 0

Factor a trinomial.
z((-4 + -1z)(8 + -5z)) = 0


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 '(-4 + -1z)' equal to zero and attempt to solve:

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4

Subproblem 3
Set the factor '(8 + -5z)' equal to zero and attempt to solve:

Simplifying
8 + -5z = 0

Solving
8 + -5z = 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 + -5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -5z = 0 + -8
-5z = 0 + -8

Combine like terms: 0 + -8 = -8
-5z = -8

Divide each side by '-5'.
z = 1.6

Simplifying
z = 1.6
Solution
z = {0, -4, 1.6}

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