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

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

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

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

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

Multiply (-5 + y) * (4 + y)
(-5(4 + y) + y(4 + y)) = 0
((4 * -5 + y * -5) + y(4 + y)) = 0
((-20 + -5y) + y(4 + y)) = 0
(-20 + -5y + (4 * y + y * y)) = 0
(-20 + -5y + (4y + y2)) = 0

Combine like terms: -5y + 4y = -1y
(-20 + -1y + y2) = 0

Solving
-20 + -1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-4 + -1y)' equal to zero and attempt to solve:

Simplifying
-4 + -1y = 0

Solving
-4 + -1y = 0

Move all terms containing y to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -1y = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1y = 0 + 4
-1y = 0 + 4

Combine like terms: 0 + 4 = 4
-1y = 4

Divide each side by '-1'.
y = -4

Simplifying
y = -4
Subproblem 2
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
Solution
y = {-4, 5}