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

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


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

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

Multiply (8 + 5y) * (5 + -1y)
(8(5 + -1y) + 5y * (5 + -1y)) = 0
((5 * 8 + -1y * 8) + 5y * (5 + -1y)) = 0
((40 + -8y) + 5y * (5 + -1y)) = 0
(40 + -8y + (5 * 5y + -1y * 5y)) = 0
(40 + -8y + (25y + -5y2)) = 0

Combine like terms: -8y + 25y = 17y
(40 + 17y + -5y2) = 0

Solving
40 + 17y + -5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(8 + 5y) = 0


Subproblem 1
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 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 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5

Subproblem 2
Set the factor '(8 + 5y)' equal to zero and attempt to solve:

Simplifying
8 + 5y = 0

Solving
8 + 5y = 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 + 5y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 5y = 0 + -8
5y = 0 + -8

Combine like terms: 0 + -8 = -8
5y = -8

Divide each side by '5'.
y = -1.6

Simplifying
y = -1.6
Solution
y = {5, -1.6}

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