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

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

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

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

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

Multiply (-6 + Y) * (5 + Y)
(-6(5 + Y) + Y(5 + Y)) = -2Y
((5 * -6 + Y * -6) + Y(5 + Y)) = -2Y
((-30 + -6Y) + Y(5 + Y)) = -2Y
(-30 + -6Y + (5 * Y + Y * Y)) = -2Y
(-30 + -6Y + (5Y + Y2)) = -2Y

Combine like terms: -6Y + 5Y = -1Y
(-30 + -1Y + Y2) = -2Y

Solving
-30 + -1Y + Y2 = -2Y

Solving for variable 'Y'.

Reorder the terms:
-30 + -1Y + 2Y + Y2 = -2Y + 2Y

Combine like terms: -1Y + 2Y = 1Y
-30 + 1Y + Y2 = -2Y + 2Y

Combine like terms: -2Y + 2Y = 0
-30 + 1Y + Y2 = 0

Factor a trinomial.
(-6 + -1Y)(5 + -1Y) = 0

Subproblem 1
Set the factor '(-6 + -1Y)' equal to zero and attempt to solve:

Simplifying
-6 + -1Y = 0

Solving
-6 + -1Y = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1Y = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1Y = 0 + 6
-1Y = 0 + 6

Combine like terms: 0 + 6 = 6
-1Y = 6

Divide each side by '-1'.
Y = -6

Simplifying
Y = -6
Subproblem 2
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
Solution
Y = {-6, 5}