3(3y^2+6y-4)=0

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Solution for 3(3y^2+6y-4)=0 equation: 


Simplifying
3(3y2 + 6y + -4) = 0

Reorder the terms:
3(-4 + 6y + 3y2) = 0
(-4 * 3 + 6y * 3 + 3y2 * 3) = 0
(-12 + 18y + 9y2) = 0

Solving
-12 + 18y + 9y2 = 0

Solving for variable 'y'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 6y + 3y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-4 + 6y + 3y2)' equal to zero and attempt to solve:

Simplifying
-4 + 6y + 3y2 = 0

Solving
-4 + 6y + 3y2 = 0

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

Divide each side by '3'.
-1.333333333 + 2y + y2 = 0

Move the constant term to the right:

Add '1.333333333' to each side of the equation.
-1.333333333 + 2y + 1.333333333 + y2 = 0 + 1.333333333

Reorder the terms:
-1.333333333 + 1.333333333 + 2y + y2 = 0 + 1.333333333

Combine like terms: -1.333333333 + 1.333333333 = 0.000000000
0.000000000 + 2y + y2 = 0 + 1.333333333
2y + y2 = 0 + 1.333333333

Combine like terms: 0 + 1.333333333 = 1.333333333
2y + y2 = 1.333333333

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 = 1.333333333 + 1

Reorder the terms:
1 + 2y + y2 = 1.333333333 + 1

Combine like terms: 1.333333333 + 1 = 2.333333333
1 + 2y + y2 = 2.333333333

Factor a perfect square on the left side:
(y + 1)(y + 1) = 2.333333333

Calculate the square root of the right side: 1.527525232

Break this problem into two subproblems by setting 
(y + 1) equal to 1.527525232 and -1.527525232.


Subproblem 1
y + 1 = 1.527525232

Simplifying
y + 1 = 1.527525232

Reorder the terms:
1 + y = 1.527525232

Solving
1 + y = 1.527525232

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 = 1.527525232 + -1

Combine like terms: 1 + -1 = 0
0 + y = 1.527525232 + -1
y = 1.527525232 + -1

Combine like terms: 1.527525232 + -1 = 0.527525232
y = 0.527525232

Simplifying
y = 0.527525232


Subproblem 2
y + 1 = -1.527525232

Simplifying
y + 1 = -1.527525232

Reorder the terms:
1 + y = -1.527525232

Solving
1 + y = -1.527525232

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 = -1.527525232 + -1

Combine like terms: 1 + -1 = 0
0 + y = -1.527525232 + -1
y = -1.527525232 + -1

Combine like terms: -1.527525232 + -1 = -2.527525232
y = -2.527525232

Simplifying
y = -2.527525232


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {0.527525232, -2.527525232}
Solution
y = {0.527525232, -2.527525232}

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