2y(y+3)=30

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Solution for 2y(y+3)=30 equation: 


Simplifying
2y(y + 3) = 30

Reorder the terms:
2y(3 + y) = 30
(3 * 2y + y * 2y) = 30
(6y + 2y2) = 30

Solving
6y + 2y2 = 30

Solving for variable 'y'.

Reorder the terms:
-30 + 6y + 2y2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + 6y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-15 + 3y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-15 + 3y + y2)' equal to zero and attempt to solve:

Simplifying
-15 + 3y + y2 = 0

Solving
-15 + 3y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '15' to each side of the equation.
-15 + 3y + 15 + y2 = 0 + 15

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

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

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

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = 15 + 2.25

Reorder the terms:
2.25 + 3y + y2 = 15 + 2.25

Combine like terms: 15 + 2.25 = 17.25
2.25 + 3y + y2 = 17.25

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = 17.25

Calculate the square root of the right side: 4.153311931

Break this problem into two subproblems by setting 
(y + 1.5) equal to 4.153311931 and -4.153311931.


Subproblem 1
y + 1.5 = 4.153311931

Simplifying
y + 1.5 = 4.153311931

Reorder the terms:
1.5 + y = 4.153311931

Solving
1.5 + y = 4.153311931

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = 4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = 4.153311931 + -1.5
y = 4.153311931 + -1.5

Combine like terms: 4.153311931 + -1.5 = 2.653311931
y = 2.653311931

Simplifying
y = 2.653311931


Subproblem 2
y + 1.5 = -4.153311931

Simplifying
y + 1.5 = -4.153311931

Reorder the terms:
1.5 + y = -4.153311931

Solving
1.5 + y = -4.153311931

Solving for variable 'y'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + y = -4.153311931 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + y = -4.153311931 + -1.5
y = -4.153311931 + -1.5

Combine like terms: -4.153311931 + -1.5 = -5.653311931
y = -5.653311931

Simplifying
y = -5.653311931


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {2.653311931, -5.653311931}
Solution
y = {2.653311931, -5.653311931}

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