5y(y+2)+6=3

Solution for 5y(y+2)+6=3 equation:

Simplifying
5y(y + 2) + 6 = 3

Reorder the terms:
5y(2 + y) + 6 = 3
(2 * 5y + y * 5y) + 6 = 3
(10y + 5y2) + 6 = 3

Reorder the terms:
6 + 10y + 5y2 = 3

Solving
6 + 10y + 5y2 = 3

Solving for variable 'y'.

Reorder the terms:
6 + -3 + 10y + 5y2 = 3 + -3

Combine like terms: 6 + -3 = 3
3 + 10y + 5y2 = 3 + -3

Combine like terms: 3 + -3 = 0
3 + 10y + 5y2 = 0

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

Divide each side by '5'.
0.6 + 2y + y2 = 0

Move the constant term to the right:

Add '-0.6' to each side of the equation.
0.6 + 2y + -0.6 + y2 = 0 + -0.6

Reorder the terms:
0.6 + -0.6 + 2y + y2 = 0 + -0.6

Combine like terms: 0.6 + -0.6 = 0.0
0.0 + 2y + y2 = 0 + -0.6
2y + y2 = 0 + -0.6

Combine like terms: 0 + -0.6 = -0.6
2y + y2 = -0.6

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -0.6 + 1

Reorder the terms:
1 + 2y + y2 = -0.6 + 1

Combine like terms: -0.6 + 1 = 0.4
1 + 2y + y2 = 0.4

Factor a perfect square on the left side:
(y + 1)(y + 1) = 0.4

Calculate the square root of the right side: 0.632455532

Break this problem into two subproblems by setting 
(y + 1) equal to 0.632455532 and -0.632455532.

Subproblem 1
y + 1 = 0.632455532

Simplifying
y + 1 = 0.632455532

Reorder the terms:
1 + y = 0.632455532

Solving
1 + y = 0.632455532

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = 0.632455532 + -1

Combine like terms: 1 + -1 = 0
0 + y = 0.632455532 + -1
y = 0.632455532 + -1

Combine like terms: 0.632455532 + -1 = -0.367544468
y = -0.367544468

Simplifying
y = -0.367544468

Subproblem 2
y + 1 = -0.632455532

Simplifying
y + 1 = -0.632455532

Reorder the terms:
1 + y = -0.632455532

Solving
1 + y = -0.632455532

Solving for variable 'y'.

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

Add '-1' to each side of the equation.
1 + -1 + y = -0.632455532 + -1

Combine like terms: 1 + -1 = 0
0 + y = -0.632455532 + -1
y = -0.632455532 + -1

Combine like terms: -0.632455532 + -1 = -1.632455532
y = -1.632455532

Simplifying
y = -1.632455532

Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.367544468, -1.632455532}