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

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


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

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

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

Multiply (-4 + 5z) * (5 + z)
z(-4(5 + z) + 5z * (5 + z)) = 0
z((5 * -4 + z * -4) + 5z * (5 + z)) = 0
z((-20 + -4z) + 5z * (5 + z)) = 0
z(-20 + -4z + (5 * 5z + z * 5z)) = 0
z(-20 + -4z + (25z + 5z2)) = 0

Combine like terms: -4z + 25z = 21z
z(-20 + 21z + 5z2) = 0
(-20 * z + 21z * z + 5z2 * z) = 0
(-20z + 21z2 + 5z3) = 0

Solving
-20z + 21z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), 'z'.
z(-20 + 21z + 5z2) = 0

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

Simplifying
4 + -5z = 0

Solving
4 + -5z = 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 + -5z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -5z = 0 + -4
-5z = 0 + -4

Combine like terms: 0 + -4 = -4
-5z = -4

Divide each side by '-5'.
z = 0.8

Simplifying
z = 0.8
Solution
z = {0, -5, 0.8}

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