(y-5)(y+2)=-6

Solution for (y-5)(y+2)=-6 equation:

Simplifying
(y + -5)(y + 2) = -6

Reorder the terms:
(-5 + y)(y + 2) = -6

Reorder the terms:
(-5 + y)(2 + y) = -6

Multiply (-5 + y) * (2 + y)
(-5(2 + y) + y(2 + y)) = -6
((2 * -5 + y * -5) + y(2 + y)) = -6
((-10 + -5y) + y(2 + y)) = -6
(-10 + -5y + (2 * y + y * y)) = -6
(-10 + -5y + (2y + y2)) = -6

Combine like terms: -5y + 2y = -3y
(-10 + -3y + y2) = -6

Solving
-10 + -3y + y2 = -6

Solving for variable 'y'.

Reorder the terms:
-10 + 6 + -3y + y2 = -6 + 6

Combine like terms: -10 + 6 = -4
-4 + -3y + y2 = -6 + 6

Combine like terms: -6 + 6 = 0
-4 + -3y + y2 = 0

Factor a trinomial.
(-1 + -1y)(4 + -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 '(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 = {-1, 4}