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

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


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

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

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

Combine like terms: 5z + -8z = -3z
(8 + -3z + -5z2) = 0

Solving
8 + -3z + -5z2 = 0

Solving for variable 'z'.

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + 5z)' equal to zero and attempt to solve:

Simplifying
8 + 5z = 0

Solving
8 + 5z = 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 + 5z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5z = 0 + -8
5z = 0 + -8

Combine like terms: 0 + -8 = -8
5z = -8

Divide each side by '5'.
z = -1.6

Simplifying
z = -1.6
Solution
z = {1, -1.6}

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