(y-5)(y+8)=-22

Solution for (y-5)(y+8)=-22 equation:

Simplifying
(y + -5)(y + 8) = -22

Reorder the terms:
(-5 + y)(y + 8) = -22

Reorder the terms:
(-5 + y)(8 + y) = -22

Multiply (-5 + y) * (8 + y)
(-5(8 + y) + y(8 + y)) = -22
((8 * -5 + y * -5) + y(8 + y)) = -22
((-40 + -5y) + y(8 + y)) = -22
(-40 + -5y + (8 * y + y * y)) = -22
(-40 + -5y + (8y + y2)) = -22

Combine like terms: -5y + 8y = 3y
(-40 + 3y + y2) = -22

Solving
-40 + 3y + y2 = -22

Solving for variable 'y'.

Reorder the terms:
-40 + 22 + 3y + y2 = -22 + 22

Combine like terms: -40 + 22 = -18
-18 + 3y + y2 = -22 + 22

Combine like terms: -22 + 22 = 0
-18 + 3y + y2 = 0

Factor a trinomial.
(-6 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-6 + -1y)' equal to zero and attempt to solve:

Simplifying
-6 + -1y = 0

Solving
-6 + -1y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1y = 0 + 6
-1y = 0 + 6

Combine like terms: 0 + 6 = 6
-1y = 6

Divide each side by '-1'.
y = -6

Simplifying
y = -6
Subproblem 2
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
Solution
y = {-6, 3}