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

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Solution for (4+z)(5z-8)=0 equation: 


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

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

Multiply (4 + z) * (-8 + 5z)
(4(-8 + 5z) + z(-8 + 5z)) = 0
((-8 * 4 + 5z * 4) + z(-8 + 5z)) = 0
((-32 + 20z) + z(-8 + 5z)) = 0
(-32 + 20z + (-8 * z + 5z * z)) = 0
(-32 + 20z + (-8z + 5z2)) = 0

Combine like terms: 20z + -8z = 12z
(-32 + 12z + 5z2) = 0

Solving
-32 + 12z + 5z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-4 + -1z)(8 + -5z) = 0


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

Simplifying
-4 + -1z = 0

Solving
-4 + -1z = 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 + -1z = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1z = 0 + 4
-1z = 0 + 4

Combine like terms: 0 + 4 = 4
-1z = 4

Divide each side by '-1'.
z = -4

Simplifying
z = -4

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 = {-4, 1.6}

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