(y+8)(y-9)=-52

Solution for (y+8)(y-9)=-52 equation:

Simplifying
(y + 8)(y + -9) = -52

Reorder the terms:
(8 + y)(y + -9) = -52

Reorder the terms:
(8 + y)(-9 + y) = -52

Multiply (8 + y) * (-9 + y)
(8(-9 + y) + y(-9 + y)) = -52
((-9 * 8 + y * 8) + y(-9 + y)) = -52
((-72 + 8y) + y(-9 + y)) = -52
(-72 + 8y + (-9 * y + y * y)) = -52
(-72 + 8y + (-9y + y2)) = -52

Combine like terms: 8y + -9y = -1y
(-72 + -1y + y2) = -52

Solving
-72 + -1y + y2 = -52

Solving for variable 'y'.

Reorder the terms:
-72 + 52 + -1y + y2 = -52 + 52

Combine like terms: -72 + 52 = -20
-20 + -1y + y2 = -52 + 52

Combine like terms: -52 + 52 = 0
-20 + -1y + y2 = 0

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}