-4z(z+1)(z-8)=0

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Solution for -4z(z+1)(z-8)=0 equation: 


Simplifying
-4z(z + 1)(z + -8) = 0

Reorder the terms:
-4z(1 + z)(z + -8) = 0

Reorder the terms:
-4z(1 + z)(-8 + z) = 0

Multiply (1 + z) * (-8 + z)
-4z(1(-8 + z) + z(-8 + z)) = 0
-4z((-8 * 1 + z * 1) + z(-8 + z)) = 0
-4z((-8 + 1z) + z(-8 + z)) = 0
-4z(-8 + 1z + (-8 * z + z * z)) = 0
-4z(-8 + 1z + (-8z + z2)) = 0

Combine like terms: 1z + -8z = -7z
-4z(-8 + -7z + z2) = 0
(-8 * -4z + -7z * -4z + z2 * -4z) = 0
(32z + 28z2 + -4z3) = 0

Solving
32z + 28z2 + -4z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(8 + 7z + -1z2) = 0

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

Ignore the factor 4.

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

Simplifying
8 + -1z = 0

Solving
8 + -1z = 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 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

Divide each side by '-1'.
z = 8

Simplifying
z = 8

Subproblem 3
Set the factor '(1 + z)' equal to zero and attempt to solve:

Simplifying
1 + z = 0

Solving
1 + z = 0

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

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

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

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

Simplifying
z = -1
Solution
z = {0, 8, -1}

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