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

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


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

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

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

Multiply (-8 + 3z) * (5 + z)
z(-8(5 + z) + 3z * (5 + z)) = 0
z((5 * -8 + z * -8) + 3z * (5 + z)) = 0
z((-40 + -8z) + 3z * (5 + z)) = 0
z(-40 + -8z + (5 * 3z + z * 3z)) = 0
z(-40 + -8z + (15z + 3z2)) = 0

Combine like terms: -8z + 15z = 7z
z(-40 + 7z + 3z2) = 0
(-40 * z + 7z * z + 3z2 * z) = 0
(-40z + 7z2 + 3z3) = 0

Solving
-40z + 7z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-40 + 7z + 3z2) = 0

Factor a trinomial.
z((-5 + -1z)(8 + -3z)) = 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 '(-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 '(8 + -3z)' equal to zero and attempt to solve:

Simplifying
8 + -3z = 0

Solving
8 + -3z = 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 + -3z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3z = 0 + -8
-3z = 0 + -8

Combine like terms: 0 + -8 = -8
-3z = -8

Divide each side by '-3'.
z = 2.666666667

Simplifying
z = 2.666666667
Solution
z = {0, -5, 2.666666667}

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