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

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


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

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

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

Multiply (5 + 4z) * (-8 + 5z)
(5(-8 + 5z) + 4z * (-8 + 5z)) = 0
((-8 * 5 + 5z * 5) + 4z * (-8 + 5z)) = 0
((-40 + 25z) + 4z * (-8 + 5z)) = 0
(-40 + 25z + (-8 * 4z + 5z * 4z)) = 0
(-40 + 25z + (-32z + 20z2)) = 0

Combine like terms: 25z + -32z = -7z
(-40 + -7z + 20z2) = 0

Solving
-40 + -7z + 20z2 = 0

Solving for variable 'z'.

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


Subproblem 1
Set the factor '(-5 + -4z)' equal to zero and attempt to solve:

Simplifying
-5 + -4z = 0

Solving
-5 + -4z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -4z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -4z = 0 + 5
-4z = 0 + 5

Combine like terms: 0 + 5 = 5
-4z = 5

Divide each side by '-4'.
z = -1.25

Simplifying
z = -1.25

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 = {-1.25, 1.6}

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