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

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


Simplifying
(2 + -1z)(3z + -8) = 0

Reorder the terms:
(2 + -1z)(-8 + 3z) = 0

Multiply (2 + -1z) * (-8 + 3z)
(2(-8 + 3z) + -1z * (-8 + 3z)) = 0
((-8 * 2 + 3z * 2) + -1z * (-8 + 3z)) = 0
((-16 + 6z) + -1z * (-8 + 3z)) = 0
(-16 + 6z + (-8 * -1z + 3z * -1z)) = 0
(-16 + 6z + (8z + -3z2)) = 0

Combine like terms: 6z + 8z = 14z
(-16 + 14z + -3z2) = 0

Solving
-16 + 14z + -3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + 3z)(2 + -1z) = 0


Subproblem 1
Set the factor '(-8 + 3z)' equal to zero and attempt to solve:

Simplifying
-8 + 3z = 0

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

Combine like terms: -8 + 8 = 0
0 + 3z = 0 + 8
3z = 0 + 8

Combine like terms: 0 + 8 = 8
3z = 8

Divide each side by '3'.
z = 2.666666667

Simplifying
z = 2.666666667

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

Simplifying
z = 2
Solution
z = {2.666666667, 2}

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