(5y-8)(7+y)=0

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Solution for (5y-8)(7+y)=0 equation: 


Simplifying
(5y + -8)(7 + y) = 0

Reorder the terms:
(-8 + 5y)(7 + y) = 0

Multiply (-8 + 5y) * (7 + y)
(-8(7 + y) + 5y * (7 + y)) = 0
((7 * -8 + y * -8) + 5y * (7 + y)) = 0
((-56 + -8y) + 5y * (7 + y)) = 0
(-56 + -8y + (7 * 5y + y * 5y)) = 0
(-56 + -8y + (35y + 5y2)) = 0

Combine like terms: -8y + 35y = 27y
(-56 + 27y + 5y2) = 0

Solving
-56 + 27y + 5y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-7 + -1y)(8 + -5y) = 0


Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 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 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7

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 = {-7, 1.6}

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