(5z-1)(8+z)=0

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Solution for (5z-1)(8+z)=0 equation: 


Simplifying
(5z + -1)(8 + z) = 0

Reorder the terms:
(-1 + 5z)(8 + z) = 0

Multiply (-1 + 5z) * (8 + z)
(-1(8 + z) + 5z * (8 + z)) = 0
((8 * -1 + z * -1) + 5z * (8 + z)) = 0
((-8 + -1z) + 5z * (8 + z)) = 0
(-8 + -1z + (8 * 5z + z * 5z)) = 0
(-8 + -1z + (40z + 5z2)) = 0

Combine like terms: -1z + 40z = 39z
(-8 + 39z + 5z2) = 0

Solving
-8 + 39z + 5z2 = 0

Solving for variable 'z'.

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


Subproblem 1
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 2
Set the factor '(1 + -5z)' equal to zero and attempt to solve:

Simplifying
1 + -5z = 0

Solving
1 + -5z = 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 + -5z = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5z = 0 + -1
-5z = 0 + -1

Combine like terms: 0 + -1 = -1
-5z = -1

Divide each side by '-5'.
z = 0.2

Simplifying
z = 0.2
Solution
z = {-8, 0.2}

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