5z^5(z-6)(z-8)=0

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Solution for 5z^5(z-6)(z-8)=0 equation: 


Simplifying
5z5(z + -6)(z + -8) = 0

Reorder the terms:
5z5(-6 + z)(z + -8) = 0

Reorder the terms:
5z5(-6 + z)(-8 + z) = 0

Multiply (-6 + z) * (-8 + z)
5z5(-6(-8 + z) + z(-8 + z)) = 0
5z5((-8 * -6 + z * -6) + z(-8 + z)) = 0
5z5((48 + -6z) + z(-8 + z)) = 0
5z5(48 + -6z + (-8 * z + z * z)) = 0
5z5(48 + -6z + (-8z + z2)) = 0

Combine like terms: -6z + -8z = -14z
5z5(48 + -14z + z2) = 0
(48 * 5z5 + -14z * 5z5 + z2 * 5z5) = 0
(240z5 + -70z6 + 5z7) = 0

Solving
240z5 + -70z6 + 5z7 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z5'.
5z5(48 + -14z + z2) = 0

Factor a trinomial.
5z5((6 + -1z)(8 + -1z)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'z5' equal to zero and attempt to solve:

Simplifying
z5 = 0

Solving
z5 = 0

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

Simplifying
z5 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6

Subproblem 3
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
Solution
z = {6, 8}

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