z(3z-5)(z+4)=0

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Solution for z(3z-5)(z+4)=0 equation: 


Simplifying
z(3z + -5)(z + 4) = 0

Reorder the terms:
z(-5 + 3z)(z + 4) = 0

Reorder the terms:
z(-5 + 3z)(4 + z) = 0

Multiply (-5 + 3z) * (4 + z)
z(-5(4 + z) + 3z * (4 + z)) = 0
z((4 * -5 + z * -5) + 3z * (4 + z)) = 0
z((-20 + -5z) + 3z * (4 + z)) = 0
z(-20 + -5z + (4 * 3z + z * 3z)) = 0
z(-20 + -5z + (12z + 3z2)) = 0

Combine like terms: -5z + 12z = 7z
z(-20 + 7z + 3z2) = 0
(-20 * z + 7z * z + 3z2 * z) = 0
(-20z + 7z2 + 3z3) = 0

Solving
-20z + 7z2 + 3z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-20 + 7z + 3z2) = 0

Factor a trinomial.
z((-4 + -1z)(5 + -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 '(-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 '(5 + -3z)' equal to zero and attempt to solve:

Simplifying
5 + -3z = 0

Solving
5 + -3z = 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 + -3z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3z = 0 + -5
-3z = 0 + -5

Combine like terms: 0 + -5 = -5
-3z = -5

Divide each side by '-3'.
z = 1.666666667

Simplifying
z = 1.666666667
Solution
z = {0, -4, 1.666666667}

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