2(11-3y)+y^2=14

Solution for 2(11-3y)+y^2=14 equation:

Simplifying
2(11 + -3y) + y2 = 14
(11 * 2 + -3y * 2) + y2 = 14
(22 + -6y) + y2 = 14

Solving
22 + -6y + y2 = 14

Solving for variable 'y'.

Reorder the terms:
22 + -14 + -6y + y2 = 14 + -14

Combine like terms: 22 + -14 = 8
8 + -6y + y2 = 14 + -14

Combine like terms: 14 + -14 = 0
8 + -6y + y2 = 0

Factor a trinomial.
(2 + -1y)(4 + -1y) = 0

Subproblem 1
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
Subproblem 2
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
Solution
y = {2, 4}