15y+14=2y(5y+6)

Solution for 15y+14=2y(5y+6) equation:

Simplifying
15y + 14 = 2y(5y + 6)

Reorder the terms:
14 + 15y = 2y(5y + 6)

Reorder the terms:
14 + 15y = 2y(6 + 5y)
14 + 15y = (6 * 2y + 5y * 2y)
14 + 15y = (12y + 10y2)

Solving
14 + 15y = 12y + 10y2

Solving for variable 'y'.

Combine like terms: 15y + -12y = 3y
14 + 3y + -10y2 = 12y + 10y2 + -12y + -10y2

Reorder the terms:
14 + 3y + -10y2 = 12y + -12y + 10y2 + -10y2

Combine like terms: 12y + -12y = 0
14 + 3y + -10y2 = 0 + 10y2 + -10y2
14 + 3y + -10y2 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
14 + 3y + -10y2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-1.4 + -0.3y + y2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -0.3y + 1.4 + y2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -0.3y + y2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -0.3y + y2 = 0 + 1.4
-0.3y + y2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-0.3y + y2 = 1.4

The y term is -0.3y.  Take half its coefficient (-0.15).
Square it (0.0225) and add it to both sides.

Add '0.0225' to each side of the equation.
-0.3y + 0.0225 + y2 = 1.4 + 0.0225

Reorder the terms:
0.0225 + -0.3y + y2 = 1.4 + 0.0225

Combine like terms: 1.4 + 0.0225 = 1.4225
0.0225 + -0.3y + y2 = 1.4225

Factor a perfect square on the left side:
(y + -0.15)(y + -0.15) = 1.4225

Calculate the square root of the right side: 1.192686044

Break this problem into two subproblems by setting 
(y + -0.15) equal to 1.192686044 and -1.192686044.

Subproblem 1
y + -0.15 = 1.192686044

Simplifying
y + -0.15 = 1.192686044

Reorder the terms:
-0.15 + y = 1.192686044

Solving
-0.15 + y = 1.192686044

Solving for variable 'y'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + y = 1.192686044 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + y = 1.192686044 + 0.15
y = 1.192686044 + 0.15

Combine like terms: 1.192686044 + 0.15 = 1.342686044
y = 1.342686044

Simplifying
y = 1.342686044

Subproblem 2
y + -0.15 = -1.192686044

Simplifying
y + -0.15 = -1.192686044

Reorder the terms:
-0.15 + y = -1.192686044

Solving
-0.15 + y = -1.192686044

Solving for variable 'y'.

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

Add '0.15' to each side of the equation.
-0.15 + 0.15 + y = -1.192686044 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + y = -1.192686044 + 0.15
y = -1.192686044 + 0.15

Combine like terms: -1.192686044 + 0.15 = -1.042686044
y = -1.042686044

Simplifying
y = -1.042686044

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.342686044, -1.042686044}