5(Z-4)(-Z+1)=0

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Solution for 5(Z-4)(-Z+1)=0 equation: 


Simplifying
5(Z + -4)(-1Z + 1) = 0

Reorder the terms:
5(-4 + Z)(-1Z + 1) = 0

Reorder the terms:
5(-4 + Z)(1 + -1Z) = 0

Multiply (-4 + Z) * (1 + -1Z)
5(-4(1 + -1Z) + Z(1 + -1Z)) = 0
5((1 * -4 + -1Z * -4) + Z(1 + -1Z)) = 0
5((-4 + 4Z) + Z(1 + -1Z)) = 0
5(-4 + 4Z + (1 * Z + -1Z * Z)) = 0
5(-4 + 4Z + (1Z + -1Z2)) = 0

Combine like terms: 4Z + 1Z = 5Z
5(-4 + 5Z + -1Z2) = 0
(-4 * 5 + 5Z * 5 + -1Z2 * 5) = 0
(-20 + 25Z + -5Z2) = 0

Solving
-20 + 25Z + -5Z2 = 0

Solving for variable 'Z'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-4 + 5Z + -1Z2) = 0

Factor a trinomial.
5((-4 + Z)(1 + -1Z)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-4 + Z)' equal to zero and attempt to solve:

Simplifying
-4 + Z = 0

Solving
-4 + Z = 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 + Z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + Z = 0 + 4
Z = 0 + 4

Combine like terms: 0 + 4 = 4
Z = 4

Simplifying
Z = 4

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

Simplifying
1 + -1Z = 0

Solving
1 + -1Z = 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 + -1Z = 0 + -1

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

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

Divide each side by '-1'.
Z = 1

Simplifying
Z = 1
Solution
Z = {4, 1}

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