(2y-7)(8-y)=0

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Solution for (2y-7)(8-y)=0 equation: 


Simplifying
(2y + -7)(8 + -1y) = 0

Reorder the terms:
(-7 + 2y)(8 + -1y) = 0

Multiply (-7 + 2y) * (8 + -1y)
(-7(8 + -1y) + 2y * (8 + -1y)) = 0
((8 * -7 + -1y * -7) + 2y * (8 + -1y)) = 0
((-56 + 7y) + 2y * (8 + -1y)) = 0
(-56 + 7y + (8 * 2y + -1y * 2y)) = 0
(-56 + 7y + (16y + -2y2)) = 0

Combine like terms: 7y + 16y = 23y
(-56 + 23y + -2y2) = 0

Solving
-56 + 23y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-8 + y)(7 + -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 '(7 + -2y)' equal to zero and attempt to solve:

Simplifying
7 + -2y = 0

Solving
7 + -2y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -2y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2y = 0 + -7
-2y = 0 + -7

Combine like terms: 0 + -7 = -7
-2y = -7

Divide each side by '-2'.
y = 3.5

Simplifying
y = 3.5
Solution
y = {8, 3.5}

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