(y+2)(y-4)=-5

Solution for (y+2)(y-4)=-5 equation:

Simplifying
(y + 2)(y + -4) = -5

Reorder the terms:
(2 + y)(y + -4) = -5

Reorder the terms:
(2 + y)(-4 + y) = -5

Multiply (2 + y) * (-4 + y)
(2(-4 + y) + y(-4 + y)) = -5
((-4 * 2 + y * 2) + y(-4 + y)) = -5
((-8 + 2y) + y(-4 + y)) = -5
(-8 + 2y + (-4 * y + y * y)) = -5
(-8 + 2y + (-4y + y2)) = -5

Combine like terms: 2y + -4y = -2y
(-8 + -2y + y2) = -5

Solving
-8 + -2y + y2 = -5

Solving for variable 'y'.

Reorder the terms:
-8 + 5 + -2y + y2 = -5 + 5

Combine like terms: -8 + 5 = -3
-3 + -2y + y2 = -5 + 5

Combine like terms: -5 + 5 = 0
-3 + -2y + y2 = 0

Factor a trinomial.
(-1 + -1y)(3 + -1y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 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 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Solution
y = {-1, 3}