(y+5)(y-1)=27

Solution for (y+5)(y-1)=27 equation:

Simplifying
(y + 5)(y + -1) = 27

Reorder the terms:
(5 + y)(y + -1) = 27

Reorder the terms:
(5 + y)(-1 + y) = 27

Multiply (5 + y) * (-1 + y)
(5(-1 + y) + y(-1 + y)) = 27
((-1 * 5 + y * 5) + y(-1 + y)) = 27
((-5 + 5y) + y(-1 + y)) = 27
(-5 + 5y + (-1 * y + y * y)) = 27
(-5 + 5y + (-1y + y2)) = 27

Combine like terms: 5y + -1y = 4y
(-5 + 4y + y2) = 27

Solving
-5 + 4y + y2 = 27

Solving for variable 'y'.

Reorder the terms:
-5 + -27 + 4y + y2 = 27 + -27

Combine like terms: -5 + -27 = -32
-32 + 4y + y2 = 27 + -27

Combine like terms: 27 + -27 = 0
-32 + 4y + y2 = 0

Factor a trinomial.
(-8 + -1y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
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 = {-8, 4}