2y+2(y^2+1)=14

Solution for 2y+2(y^2+1)=14 equation:

Simplifying
2y + 2(y2 + 1) = 14

Reorder the terms:
2y + 2(1 + y2) = 14
2y + (1 * 2 + y2 * 2) = 14
2y + (2 + 2y2) = 14

Reorder the terms:
2 + 2y + 2y2 = 14

Solving
2 + 2y + 2y2 = 14

Solving for variable 'y'.

Reorder the terms:
2 + -14 + 2y + 2y2 = 14 + -14

Combine like terms: 2 + -14 = -12
-12 + 2y + 2y2 = 14 + -14

Combine like terms: 14 + -14 = 0
-12 + 2y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + y + y2) = 0

Factor a trinomial.
2((-3 + -1y)(2 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -1y)' equal to zero and attempt to solve:

Simplifying
-3 + -1y = 0

Solving
-3 + -1y = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1y = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1y = 0 + 3
-1y = 0 + 3

Combine like terms: 0 + 3 = 3
-1y = 3

Divide each side by '-1'.
y = -3

Simplifying
y = -3
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 = {-3, 2}