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

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


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

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

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

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

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

Solving for variable 'y'.

Combine like terms: 0 + 8 = 8
8 + -17y + 2y2 = -8 + 17y + -2y2 + 8 + -17y + 2y2

Reorder the terms:
8 + -17y + 2y2 = -8 + 8 + 17y + -17y + -2y2 + 2y2

Combine like terms: -8 + 8 = 0
8 + -17y + 2y2 = 0 + 17y + -17y + -2y2 + 2y2
8 + -17y + 2y2 = 17y + -17y + -2y2 + 2y2

Combine like terms: 17y + -17y = 0
8 + -17y + 2y2 = 0 + -2y2 + 2y2
8 + -17y + 2y2 = -2y2 + 2y2

Combine like terms: -2y2 + 2y2 = 0
8 + -17y + 2y2 = 0

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


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -1y)' equal to zero and attempt to solve:

Simplifying
8 + -1y = 0

Solving
8 + -1y = 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 + -1y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1y = 0 + -8
-1y = 0 + -8

Combine like terms: 0 + -8 = -8
-1y = -8

Divide each side by '-1'.
y = 8

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

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