(4y+5)(8-y)=0

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Solution for (4y+5)(8-y)=0 equation: 


Simplifying
(4y + 5)(8 + -1y) = 0

Reorder the terms:
(5 + 4y)(8 + -1y) = 0

Multiply (5 + 4y) * (8 + -1y)
(5(8 + -1y) + 4y * (8 + -1y)) = 0
((8 * 5 + -1y * 5) + 4y * (8 + -1y)) = 0
((40 + -5y) + 4y * (8 + -1y)) = 0
(40 + -5y + (8 * 4y + -1y * 4y)) = 0
(40 + -5y + (32y + -4y2)) = 0

Combine like terms: -5y + 32y = 27y
(40 + 27y + -4y2) = 0

Solving
40 + 27y + -4y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(8 + -1y)(5 + 4y) = 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 '(5 + 4y)' equal to zero and attempt to solve:

Simplifying
5 + 4y = 0

Solving
5 + 4y = 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 + 4y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4y = 0 + -5
4y = 0 + -5

Combine like terms: 0 + -5 = -5
4y = -5

Divide each side by '4'.
y = -1.25

Simplifying
y = -1.25
Solution
y = {8, -1.25}

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