2y(y+6)=10

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Solution for 2y(y+6)=10 equation: 


Simplifying
2y(y + 6) = 10

Reorder the terms:
2y(6 + y) = 10
(6 * 2y + y * 2y) = 10
(12y + 2y2) = 10

Solving
12y + 2y2 = 10

Solving for variable 'y'.

Reorder the terms:
-10 + 12y + 2y2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 12y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + 6y + y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-5 + 6y + y2)' equal to zero and attempt to solve:

Simplifying
-5 + 6y + y2 = 0

Solving
-5 + 6y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6y + 5 + y2 = 0 + 5

Reorder the terms:
-5 + 5 + 6y + y2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 6y + y2 = 0 + 5
6y + y2 = 0 + 5

Combine like terms: 0 + 5 = 5
6y + y2 = 5

The y term is 6y.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6y + 9 + y2 = 5 + 9

Reorder the terms:
9 + 6y + y2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6y + y2 = 14

Factor a perfect square on the left side:
(y + 3)(y + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(y + 3) equal to 3.741657387 and -3.741657387.


Subproblem 1
y + 3 = 3.741657387

Simplifying
y + 3 = 3.741657387

Reorder the terms:
3 + y = 3.741657387

Solving
3 + y = 3.741657387

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + y = 3.741657387 + -3
y = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
y = 0.741657387

Simplifying
y = 0.741657387


Subproblem 2
y + 3 = -3.741657387

Simplifying
y + 3 = -3.741657387

Reorder the terms:
3 + y = -3.741657387

Solving
3 + y = -3.741657387

Solving for variable 'y'.

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

Add '-3' to each side of the equation.
3 + -3 + y = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + y = -3.741657387 + -3
y = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
y = -6.741657387

Simplifying
y = -6.741657387


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.741657387, -6.741657387}
Solution
y = {0.741657387, -6.741657387}

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