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

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


Simplifying
-5(y + 8)(-1y + 7) = 0

Reorder the terms:
-5(8 + y)(-1y + 7) = 0

Reorder the terms:
-5(8 + y)(7 + -1y) = 0

Multiply (8 + y) * (7 + -1y)
-5(8(7 + -1y) + y(7 + -1y)) = 0
-5((7 * 8 + -1y * 8) + y(7 + -1y)) = 0
-5((56 + -8y) + y(7 + -1y)) = 0
-5(56 + -8y + (7 * y + -1y * y)) = 0
-5(56 + -8y + (7y + -1y2)) = 0

Combine like terms: -8y + 7y = -1y
-5(56 + -1y + -1y2) = 0
(56 * -5 + -1y * -5 + -1y2 * -5) = 0
(-280 + 5y + 5y2) = 0

Solving
-280 + 5y + 5y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-56 + y + y2) = 0

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

Ignore the factor 5.

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 + -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
Solution
y = {-8, 7}

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