5y(2y+3)+(2y-3)=

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Solution for 5y(2y+3)+(2y-3)= equation: 


Simplifying
5y(2y + 3) + (2y + -3) = 0

Reorder the terms:
5y(3 + 2y) + (2y + -3) = 0
(3 * 5y + 2y * 5y) + (2y + -3) = 0
(15y + 10y2) + (2y + -3) = 0

Reorder the terms:
15y + 10y2 + (-3 + 2y) = 0

Remove parenthesis around (-3 + 2y)
15y + 10y2 + -3 + 2y = 0

Reorder the terms:
-3 + 15y + 2y + 10y2 = 0

Combine like terms: 15y + 2y = 17y
-3 + 17y + 10y2 = 0

Solving
-3 + 17y + 10y2 = 0

Solving for variable 'y'.

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

Divide each side by '10'.
-0.3 + 1.7y + y2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + 1.7y + 0.3 + y2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + 1.7y + y2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + 1.7y + y2 = 0.0 + 0.3
1.7y + y2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
1.7y + y2 = 0.3

The y term is 1.7y.  Take half its coefficient (0.85).
Square it (0.7225) and add it to both sides.

Add '0.7225' to each side of the equation.
1.7y + 0.7225 + y2 = 0.3 + 0.7225

Reorder the terms:
0.7225 + 1.7y + y2 = 0.3 + 0.7225

Combine like terms: 0.3 + 0.7225 = 1.0225
0.7225 + 1.7y + y2 = 1.0225

Factor a perfect square on the left side:
(y + 0.85)(y + 0.85) = 1.0225

Calculate the square root of the right side: 1.011187421

Break this problem into two subproblems by setting 
(y + 0.85) equal to 1.011187421 and -1.011187421.


Subproblem 1
y + 0.85 = 1.011187421

Simplifying
y + 0.85 = 1.011187421

Reorder the terms:
0.85 + y = 1.011187421

Solving
0.85 + y = 1.011187421

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = 1.011187421 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = 1.011187421 + -0.85
y = 1.011187421 + -0.85

Combine like terms: 1.011187421 + -0.85 = 0.161187421
y = 0.161187421

Simplifying
y = 0.161187421


Subproblem 2
y + 0.85 = -1.011187421

Simplifying
y + 0.85 = -1.011187421

Reorder the terms:
0.85 + y = -1.011187421

Solving
0.85 + y = -1.011187421

Solving for variable 'y'.

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

Add '-0.85' to each side of the equation.
0.85 + -0.85 + y = -1.011187421 + -0.85

Combine like terms: 0.85 + -0.85 = 0.00
0.00 + y = -1.011187421 + -0.85
y = -1.011187421 + -0.85

Combine like terms: -1.011187421 + -0.85 = -1.861187421
y = -1.861187421

Simplifying
y = -1.861187421


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.161187421, -1.861187421}

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