(y-11)(y+6)=y-11

Solution for (y-11)(y+6)=y-11 equation:

Simplifying
(y + -11)(y + 6) = y + -11

Reorder the terms:
(-11 + y)(y + 6) = y + -11

Reorder the terms:
(-11 + y)(6 + y) = y + -11

Multiply (-11 + y) * (6 + y)
(-11(6 + y) + y(6 + y)) = y + -11
((6 * -11 + y * -11) + y(6 + y)) = y + -11
((-66 + -11y) + y(6 + y)) = y + -11
(-66 + -11y + (6 * y + y * y)) = y + -11
(-66 + -11y + (6y + y2)) = y + -11

Combine like terms: -11y + 6y = -5y
(-66 + -5y + y2) = y + -11

Reorder the terms:
-66 + -5y + y2 = -11 + y

Solving
-66 + -5y + y2 = -11 + y

Solving for variable 'y'.

Reorder the terms:
-66 + 11 + -5y + -1y + y2 = -11 + y + 11 + -1y

Combine like terms: -66 + 11 = -55
-55 + -5y + -1y + y2 = -11 + y + 11 + -1y

Combine like terms: -5y + -1y = -6y
-55 + -6y + y2 = -11 + y + 11 + -1y

Reorder the terms:
-55 + -6y + y2 = -11 + 11 + y + -1y

Combine like terms: -11 + 11 = 0
-55 + -6y + y2 = 0 + y + -1y
-55 + -6y + y2 = y + -1y

Combine like terms: y + -1y = 0
-55 + -6y + y2 = 0

Factor a trinomial.
(-5 + -1y)(11 + -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 '(11 + -1y)' equal to zero and attempt to solve:

Simplifying
11 + -1y = 0

Solving
11 + -1y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1y = 0 + -11
-1y = 0 + -11

Combine like terms: 0 + -11 = -11
-1y = -11

Divide each side by '-1'.
y = 11

Simplifying
y = 11
Solution
y = {-5, 11}