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

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


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

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

Multiply (5 + z) * (-8 + 3z)
(5(-8 + 3z) + z(-8 + 3z)) = 0
((-8 * 5 + 3z * 5) + z(-8 + 3z)) = 0
((-40 + 15z) + z(-8 + 3z)) = 0
(-40 + 15z + (-8 * z + 3z * z)) = 0
(-40 + 15z + (-8z + 3z2)) = 0

Combine like terms: 15z + -8z = 7z
(-40 + 7z + 3z2) = 0

Solving
-40 + 7z + 3z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(8 + -3z) = 0


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

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 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 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Divide each side by '-1'.
z = -5

Simplifying
z = -5

Subproblem 2
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
Solution
z = {-5, 2.666666667}

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