(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 = 9y
(56 + 9y + -2y2) = 0

Solving
56 + 9y + -2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y)(7 + 2y) = 0


Subproblem 1
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

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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