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

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


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

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

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

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

Combine like terms: 5y + -8y = -3y
(-40 + -3y + y2) = 0

Solving
-40 + -3y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-5 + -1y)(8 + -1y) = 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 + -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
Solution
y = {-5, 8}

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