2y(y+6)=14

Solution for 2y(y+6)=14 equation:

Simplifying
2y(y + 6) = 14

Reorder the terms:
2y(6 + y) = 14
(6 * 2y + y * 2y) = 14
(12y + 2y2) = 14

Solving
12y + 2y2 = 14

Solving for variable 'y'.

Reorder the terms:
-14 + 12y + 2y2 = 14 + -14

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 6y + y2) = 0

Factor a trinomial.
2((-7 + -1y)(1 + -1y)) = 0

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Solution
y = {-7, 1}