5y(2y+1)=7y+14

Solution for 5y(2y+1)=7y+14 equation:

Simplifying
5y(2y + 1) = 7y + 14

Reorder the terms:
5y(1 + 2y) = 7y + 14
(1 * 5y + 2y * 5y) = 7y + 14
(5y + 10y2) = 7y + 14

Reorder the terms:
5y + 10y2 = 14 + 7y

Solving
5y + 10y2 = 14 + 7y

Solving for variable 'y'.

Reorder the terms:
-14 + 5y + -7y + 10y2 = 14 + 7y + -14 + -7y

Combine like terms: 5y + -7y = -2y
-14 + -2y + 10y2 = 14 + 7y + -14 + -7y

Reorder the terms:
-14 + -2y + 10y2 = 14 + -14 + 7y + -7y

Combine like terms: 14 + -14 = 0
-14 + -2y + 10y2 = 0 + 7y + -7y
-14 + -2y + 10y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
-14 + -2y + 10y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + -1y + 5y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + -1y + 5y2)' equal to zero and attempt to solve:

Simplifying
-7 + -1y + 5y2 = 0

Solving
-7 + -1y + 5y2 = 0

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

Divide each side by '5'.
-1.4 + -0.2y + y2 = 0

Move the constant term to the right:

Add '1.4' to each side of the equation.
-1.4 + -0.2y + 1.4 + y2 = 0 + 1.4

Reorder the terms:
-1.4 + 1.4 + -0.2y + y2 = 0 + 1.4

Combine like terms: -1.4 + 1.4 = 0.0
0.0 + -0.2y + y2 = 0 + 1.4
-0.2y + y2 = 0 + 1.4

Combine like terms: 0 + 1.4 = 1.4
-0.2y + y2 = 1.4

The y term is -0.2y.  Take half its coefficient (-0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
-0.2y + 0.01 + y2 = 1.4 + 0.01

Reorder the terms:
0.01 + -0.2y + y2 = 1.4 + 0.01

Combine like terms: 1.4 + 0.01 = 1.41
0.01 + -0.2y + y2 = 1.41

Factor a perfect square on the left side:
(y + -0.1)(y + -0.1) = 1.41

Calculate the square root of the right side: 1.187434209

Break this problem into two subproblems by setting 
(y + -0.1) equal to 1.187434209 and -1.187434209.

Subproblem 1
y + -0.1 = 1.187434209

Simplifying
y + -0.1 = 1.187434209

Reorder the terms:
-0.1 + y = 1.187434209

Solving
-0.1 + y = 1.187434209

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = 1.187434209 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = 1.187434209 + 0.1
y = 1.187434209 + 0.1

Combine like terms: 1.187434209 + 0.1 = 1.287434209
y = 1.287434209

Simplifying
y = 1.287434209

Subproblem 2
y + -0.1 = -1.187434209

Simplifying
y + -0.1 = -1.187434209

Reorder the terms:
-0.1 + y = -1.187434209

Solving
-0.1 + y = -1.187434209

Solving for variable 'y'.

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

Add '0.1' to each side of the equation.
-0.1 + 0.1 + y = -1.187434209 + 0.1

Combine like terms: -0.1 + 0.1 = 0.0
0.0 + y = -1.187434209 + 0.1
y = -1.187434209 + 0.1

Combine like terms: -1.187434209 + 0.1 = -1.087434209
y = -1.087434209

Simplifying
y = -1.087434209

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.287434209, -1.087434209}
Solution
y = {1.287434209, -1.087434209}