(2y-1)(8-y)=0

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Solution for (2y-1)(8-y)=0 equation: 


Simplifying
(2y + -1)(8 + -1y) = 0

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

Multiply (-1 + 2y) * (8 + -1y)
(-1(8 + -1y) + 2y * (8 + -1y)) = 0
((8 * -1 + -1y * -1) + 2y * (8 + -1y)) = 0
((-8 + 1y) + 2y * (8 + -1y)) = 0
(-8 + 1y + (8 * 2y + -1y * 2y)) = 0
(-8 + 1y + (16y + -2y2)) = 0

Combine like terms: 1y + 16y = 17y
(-8 + 17y + -2y2) = 0

Solving
-8 + 17y + -2y2 = 0

Solving for variable 'y'.

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


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

Simplifying
-8 + y = 0

Solving
-8 + y = 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 + y = 0 + 8

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

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

Simplifying
y = 8

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

Simplifying
1 + -2y = 0

Solving
1 + -2y = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2y = 0 + -1

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

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

Divide each side by '-2'.
y = 0.5

Simplifying
y = 0.5
Solution
y = {8, 0.5}

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