5z(z-7)(z-8)=0

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Solution for 5z(z-7)(z-8)=0 equation: 


Simplifying
5z(z + -7)(z + -8) = 0

Reorder the terms:
5z(-7 + z)(z + -8) = 0

Reorder the terms:
5z(-7 + z)(-8 + z) = 0

Multiply (-7 + z) * (-8 + z)
5z(-7(-8 + z) + z(-8 + z)) = 0
5z((-8 * -7 + z * -7) + z(-8 + z)) = 0
5z((56 + -7z) + z(-8 + z)) = 0
5z(56 + -7z + (-8 * z + z * z)) = 0
5z(56 + -7z + (-8z + z2)) = 0

Combine like terms: -7z + -8z = -15z
5z(56 + -15z + z2) = 0
(56 * 5z + -15z * 5z + z2 * 5z) = 0
(280z + -75z2 + 5z3) = 0

Solving
280z + -75z2 + 5z3 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '5z'.
5z(56 + -15z + z2) = 0

Factor a trinomial.
5z((7 + -1z)(8 + -1z)) = 0

Ignore the factor 5.

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 '(7 + -1z)' equal to zero and attempt to solve:

Simplifying
7 + -1z = 0

Solving
7 + -1z = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1z = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1z = 0 + -7
-1z = 0 + -7

Combine like terms: 0 + -7 = -7
-1z = -7

Divide each side by '-1'.
z = 7

Simplifying
z = 7

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 = {0, 7, 8}

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