3(y^2+10y+3)=

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Solution for 3(y^2+10y+3)= equation: 


Simplifying
3(y2 + 10y + 3) = 0

Reorder the terms:
3(3 + 10y + y2) = 0
(3 * 3 + 10y * 3 + y2 * 3) = 0
(9 + 30y + 3y2) = 0

Solving
9 + 30y + 3y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + 10y + y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + 10y + y2)' equal to zero and attempt to solve:

Simplifying
3 + 10y + y2 = 0

Solving
3 + 10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 10y + -3 + y2 = 0 + -3

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

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

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

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = -3 + 25

Reorder the terms:
25 + 10y + y2 = -3 + 25

Combine like terms: -3 + 25 = 22
25 + 10y + y2 = 22

Factor a perfect square on the left side:
(y + 5)(y + 5) = 22

Calculate the square root of the right side: 4.69041576

Break this problem into two subproblems by setting 
(y + 5) equal to 4.69041576 and -4.69041576.


Subproblem 1
y + 5 = 4.69041576

Simplifying
y + 5 = 4.69041576

Reorder the terms:
5 + y = 4.69041576

Solving
5 + y = 4.69041576

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = 4.69041576 + -5

Combine like terms: 5 + -5 = 0
0 + y = 4.69041576 + -5
y = 4.69041576 + -5

Combine like terms: 4.69041576 + -5 = -0.30958424
y = -0.30958424

Simplifying
y = -0.30958424


Subproblem 2
y + 5 = -4.69041576

Simplifying
y + 5 = -4.69041576

Reorder the terms:
5 + y = -4.69041576

Solving
5 + y = -4.69041576

Solving for variable 'y'.

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

Add '-5' to each side of the equation.
5 + -5 + y = -4.69041576 + -5

Combine like terms: 5 + -5 = 0
0 + y = -4.69041576 + -5
y = -4.69041576 + -5

Combine like terms: -4.69041576 + -5 = -9.69041576
y = -9.69041576

Simplifying
y = -9.69041576


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {-0.30958424, -9.69041576}
Solution
y = {-0.30958424, -9.69041576}

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