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

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


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

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

Multiply (-2 + 3z) * (8 + -1z)
(-2(8 + -1z) + 3z * (8 + -1z)) = 0
((8 * -2 + -1z * -2) + 3z * (8 + -1z)) = 0
((-16 + 2z) + 3z * (8 + -1z)) = 0
(-16 + 2z + (8 * 3z + -1z * 3z)) = 0
(-16 + 2z + (24z + -3z2)) = 0

Combine like terms: 2z + 24z = 26z
(-16 + 26z + -3z2) = 0

Solving
-16 + 26z + -3z2 = 0

Solving for variable 'z'.

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


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

Simplifying
-8 + z = 0

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

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

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

Simplifying
z = 8

Subproblem 2
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
Solution
z = {8, 0.6666666667}

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