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((-1 + -1y)(7 + -1y)) = 0

Ignore the factor 2.
Subproblem 1
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
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 = {-1, 7}