(y+4)(y-3)-8=0

Solution for (y+4)(y-3)-8=0 equation:

Simplifying
(y + 4)(y + -3) + -8 = 0

Reorder the terms:
(4 + y)(y + -3) + -8 = 0

Reorder the terms:
(4 + y)(-3 + y) + -8 = 0

Multiply (4 + y) * (-3 + y)
(4(-3 + y) + y(-3 + y)) + -8 = 0
((-3 * 4 + y * 4) + y(-3 + y)) + -8 = 0
((-12 + 4y) + y(-3 + y)) + -8 = 0
(-12 + 4y + (-3 * y + y * y)) + -8 = 0
(-12 + 4y + (-3y + y2)) + -8 = 0

Combine like terms: 4y + -3y = 1y
(-12 + 1y + y2) + -8 = 0

Reorder the terms:
-12 + -8 + 1y + y2 = 0

Combine like terms: -12 + -8 = -20
-20 + 1y + y2 = 0

Solving
-20 + 1y + y2 = 0

Solving for variable 'y'.

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

Subproblem 1
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
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 = {-5, 4}