(5z-8)(3z+2)=0

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Solution for (5z-8)(3z+2)=0 equation: 


Simplifying
(5z + -8)(3z + 2) = 0

Reorder the terms:
(-8 + 5z)(3z + 2) = 0

Reorder the terms:
(-8 + 5z)(2 + 3z) = 0

Multiply (-8 + 5z) * (2 + 3z)
(-8(2 + 3z) + 5z * (2 + 3z)) = 0
((2 * -8 + 3z * -8) + 5z * (2 + 3z)) = 0
((-16 + -24z) + 5z * (2 + 3z)) = 0
(-16 + -24z + (2 * 5z + 3z * 5z)) = 0
(-16 + -24z + (10z + 15z2)) = 0

Combine like terms: -24z + 10z = -14z
(-16 + -14z + 15z2) = 0

Solving
-16 + -14z + 15z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -3z)(8 + -5z) = 0


Subproblem 1
Set the factor '(-2 + -3z)' equal to zero and attempt to solve:

Simplifying
-2 + -3z = 0

Solving
-2 + -3z = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3z = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3z = 0 + 2
-3z = 0 + 2

Combine like terms: 0 + 2 = 2
-3z = 2

Divide each side by '-3'.
z = -0.6666666667

Simplifying
z = -0.6666666667

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 = {-0.6666666667, 1.6}

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