(y+8)(y-3)=-30

Solution for (y+8)(y-3)=-30 equation:

Simplifying
(y + 8)(y + -3) = -30

Reorder the terms:
(8 + y)(y + -3) = -30

Reorder the terms:
(8 + y)(-3 + y) = -30

Multiply (8 + y) * (-3 + y)
(8(-3 + y) + y(-3 + y)) = -30
((-3 * 8 + y * 8) + y(-3 + y)) = -30
((-24 + 8y) + y(-3 + y)) = -30
(-24 + 8y + (-3 * y + y * y)) = -30
(-24 + 8y + (-3y + y2)) = -30

Combine like terms: 8y + -3y = 5y
(-24 + 5y + y2) = -30

Solving
-24 + 5y + y2 = -30

Solving for variable 'y'.

Reorder the terms:
-24 + 30 + 5y + y2 = -30 + 30

Combine like terms: -24 + 30 = 6
6 + 5y + y2 = -30 + 30

Combine like terms: -30 + 30 = 0
6 + 5y + y2 = 0

Factor a trinomial.
(3 + y)(2 + y) = 0

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

Simplifying
3 + y = 0

Solving
3 + y = 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 + y = 0 + -3

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

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

Simplifying
y = -3
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

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