3y(y+2)=15

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Solution for 3y(y+2)=15 equation: 


Simplifying
3y(y + 2) = 15

Reorder the terms:
3y(2 + y) = 15
(2 * 3y + y * 3y) = 15
(6y + 3y2) = 15

Solving
6y + 3y2 = 15

Solving for variable 'y'.

Reorder the terms:
-15 + 6y + 3y2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 6y + 3y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-5 + 2y + y2) = 0

Ignore the factor 3.

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

Simplifying
-5 + 2y + y2 = 0

Solving
-5 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 2y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 2y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 2y + y2 = 0 + 5
2y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
2y + y2 = 5

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 = 5 + 1

Reorder the terms:
1 + 2y + y2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + 2y + y2 = 6

Factor a perfect square on the left side:
(y + 1)(y + 1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(y + 1) equal to 2.449489743 and -2.449489743.


Subproblem 1
y + 1 = 2.449489743

Simplifying
y + 1 = 2.449489743

Reorder the terms:
1 + y = 2.449489743

Solving
1 + y = 2.449489743

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 = 2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + y = 2.449489743 + -1
y = 2.449489743 + -1

Combine like terms: 2.449489743 + -1 = 1.449489743
y = 1.449489743

Simplifying
y = 1.449489743


Subproblem 2
y + 1 = -2.449489743

Simplifying
y + 1 = -2.449489743

Reorder the terms:
1 + y = -2.449489743

Solving
1 + y = -2.449489743

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 = -2.449489743 + -1

Combine like terms: 1 + -1 = 0
0 + y = -2.449489743 + -1
y = -2.449489743 + -1

Combine like terms: -2.449489743 + -1 = -3.449489743
y = -3.449489743

Simplifying
y = -3.449489743


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {1.449489743, -3.449489743}
Solution
y = {1.449489743, -3.449489743}

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