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

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

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

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

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

Multiply (-5 + y) * (4 + y)
(-5(4 + y) + y(4 + y)) = -2y
((4 * -5 + y * -5) + y(4 + y)) = -2y
((-20 + -5y) + y(4 + y)) = -2y
(-20 + -5y + (4 * y + y * y)) = -2y
(-20 + -5y + (4y + y2)) = -2y

Combine like terms: -5y + 4y = -1y
(-20 + -1y + y2) = -2y

Solving
-20 + -1y + y2 = -2y

Solving for variable 'y'.

Reorder the terms:
-20 + -1y + 2y + y2 = -2y + 2y

Combine like terms: -1y + 2y = 1y
-20 + 1y + y2 = -2y + 2y

Combine like terms: -2y + 2y = 0
-20 + 1y + y2 = 0

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}