Y(Y+11)=26

Solution for Y(Y+11)=26 equation:

Simplifying
Y(Y + 11) = 26

Reorder the terms:
Y(11 + Y) = 26
(11 * Y + Y * Y) = 26
(11Y + Y2) = 26

Solving
11Y + Y2 = 26

Solving for variable 'Y'.

Reorder the terms:
-26 + 11Y + Y2 = 26 + -26

Combine like terms: 26 + -26 = 0
-26 + 11Y + Y2 = 0

Factor a trinomial.
(-13 + -1Y)(2 + -1Y) = 0

Subproblem 1
Set the factor '(-13 + -1Y)' equal to zero and attempt to solve:

Simplifying
-13 + -1Y = 0

Solving
-13 + -1Y = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1Y = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1Y = 0 + 13
-1Y = 0 + 13

Combine like terms: 0 + 13 = 13
-1Y = 13

Divide each side by '-1'.
Y = -13

Simplifying
Y = -13
Subproblem 2
Set the factor '(2 + -1Y)' equal to zero and attempt to solve:

Simplifying
2 + -1Y = 0

Solving
2 + -1Y = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1Y = 0 + -2

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

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

Divide each side by '-1'.
Y = 2

Simplifying
Y = 2
Solution
Y = {-13, 2}