(y-6)(y+2)+5y=0

Solution for (y-6)(y+2)+5y=0 equation:

Simplifying
(y + -6)(y + 2) + 5y = 0

Reorder the terms:
(-6 + y)(y + 2) + 5y = 0

Reorder the terms:
(-6 + y)(2 + y) + 5y = 0

Multiply (-6 + y) * (2 + y)
(-6(2 + y) + y(2 + y)) + 5y = 0
((2 * -6 + y * -6) + y(2 + y)) + 5y = 0
((-12 + -6y) + y(2 + y)) + 5y = 0
(-12 + -6y + (2 * y + y * y)) + 5y = 0
(-12 + -6y + (2y + y2)) + 5y = 0

Combine like terms: -6y + 2y = -4y
(-12 + -4y + y2) + 5y = 0

Reorder the terms:
-12 + -4y + 5y + y2 = 0

Combine like terms: -4y + 5y = 1y
-12 + 1y + y2 = 0

Solving
-12 + 1y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(-4 + -1y)(3 + -1y) = 0

Subproblem 1
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
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 = {-4, 3}