(y+4)(y-1)=24

Solution for (y+4)(y-1)=24 equation:

Simplifying
(y + 4)(y + -1) = 24

Reorder the terms:
(4 + y)(y + -1) = 24

Reorder the terms:
(4 + y)(-1 + y) = 24

Multiply (4 + y) * (-1 + y)
(4(-1 + y) + y(-1 + y)) = 24
((-1 * 4 + y * 4) + y(-1 + y)) = 24
((-4 + 4y) + y(-1 + y)) = 24
(-4 + 4y + (-1 * y + y * y)) = 24
(-4 + 4y + (-1y + y2)) = 24

Combine like terms: 4y + -1y = 3y
(-4 + 3y + y2) = 24

Solving
-4 + 3y + y2 = 24

Solving for variable 'y'.

Reorder the terms:
-4 + -24 + 3y + y2 = 24 + -24

Combine like terms: -4 + -24 = -28
-28 + 3y + y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-28 + 3y + y2 = 0

Factor a trinomial.
(-7 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-7 + -1y)' equal to zero and attempt to solve:

Simplifying
-7 + -1y = 0

Solving
-7 + -1y = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1y = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1y = 0 + 7
-1y = 0 + 7

Combine like terms: 0 + 7 = 7
-1y = 7

Divide each side by '-1'.
y = -7

Simplifying
y = -7
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 = {-7, 4}