(y-5)(y+4)=-8

Solution for (y-5)(y+4)=-8 equation:

Simplifying
(y + -5)(y + 4) = -8

Reorder the terms:
(-5 + y)(y + 4) = -8

Reorder the terms:
(-5 + y)(4 + y) = -8

Multiply (-5 + y) * (4 + y)
(-5(4 + y) + y(4 + y)) = -8
((4 * -5 + y * -5) + y(4 + y)) = -8
((-20 + -5y) + y(4 + y)) = -8
(-20 + -5y + (4 * y + y * y)) = -8
(-20 + -5y + (4y + y2)) = -8

Combine like terms: -5y + 4y = -1y
(-20 + -1y + y2) = -8

Solving
-20 + -1y + y2 = -8

Solving for variable 'y'.

Reorder the terms:
-20 + 8 + -1y + y2 = -8 + 8

Combine like terms: -20 + 8 = -12
-12 + -1y + y2 = -8 + 8

Combine like terms: -8 + 8 = 0
-12 + -1y + y2 = 0

Factor a trinomial.
(-3 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
Subproblem 2
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
Solution
y = {-3, 4}