8z^2-82z+195=0

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Solution for 8z^2-82z+195=0 equation: 


Simplifying
8z2 + -82z + 195 = 0

Reorder the terms:
195 + -82z + 8z2 = 0

Solving
195 + -82z + 8z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(15 + -4z)(13 + -2z) = 0


Subproblem 1
Set the factor '(15 + -4z)' equal to zero and attempt to solve:

Simplifying
15 + -4z = 0

Solving
15 + -4z = 0

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

Add '-15' to each side of the equation.
15 + -15 + -4z = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -4z = 0 + -15
-4z = 0 + -15

Combine like terms: 0 + -15 = -15
-4z = -15

Divide each side by '-4'.
z = 3.75

Simplifying
z = 3.75

Subproblem 2
Set the factor '(13 + -2z)' equal to zero and attempt to solve:

Simplifying
13 + -2z = 0

Solving
13 + -2z = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2z = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2z = 0 + -13
-2z = 0 + -13

Combine like terms: 0 + -13 = -13
-2z = -13

Divide each side by '-2'.
z = 6.5

Simplifying
z = 6.5
Solution
z = {3.75, 6.5}

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