y(6+y)=91

Solution for y(6+y)=91 equation:

Simplifying
y(6 + y) = 91
(6 * y + y * y) = 91
(6y + y2) = 91

Solving
6y + y2 = 91

Solving for variable 'y'.

Reorder the terms:
-91 + 6y + y2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + 6y + y2 = 0

Factor a trinomial.
(-13 + -1y)(7 + -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 '(7 + -1y)' equal to zero and attempt to solve:

Simplifying
7 + -1y = 0

Solving
7 + -1y = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7

Combine like terms: 0 + -7 = -7
-1y = -7

Divide each side by '-1'.
y = 7

Simplifying
y = 7
Solution
y = {-13, 7}