(5-y)(3y-8)=0

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


Simplifying
(5 + -1y)(3y + -8) = 0

Reorder the terms:
(5 + -1y)(-8 + 3y) = 0

Multiply (5 + -1y) * (-8 + 3y)
(5(-8 + 3y) + -1y * (-8 + 3y)) = 0
((-8 * 5 + 3y * 5) + -1y * (-8 + 3y)) = 0
((-40 + 15y) + -1y * (-8 + 3y)) = 0
(-40 + 15y + (-8 * -1y + 3y * -1y)) = 0
(-40 + 15y + (8y + -3y2)) = 0

Combine like terms: 15y + 8y = 23y
(-40 + 23y + -3y2) = 0

Solving
-40 + 23y + -3y2 = 0

Solving for variable 'y'.

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


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

Simplifying
-5 + y = 0

Solving
-5 + y = 0

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

Add '5' to each side of the equation.
-5 + 5 + y = 0 + 5

Combine like terms: -5 + 5 = 0
0 + y = 0 + 5
y = 0 + 5

Combine like terms: 0 + 5 = 5
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(8 + -3y)' equal to zero and attempt to solve:

Simplifying
8 + -3y = 0

Solving
8 + -3y = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3y = 0 + -8

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

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

Divide each side by '-3'.
y = 2.666666667

Simplifying
y = 2.666666667
Solution
y = {5, 2.666666667}

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