3y^2-12y-9=0

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Solution for 3y^2-12y-9=0 equation: 


Simplifying
3y2 + -12y + -9 = 0

Reorder the terms:
-9 + -12y + 3y2 = 0

Solving
-9 + -12y + 3y2 = 0

Solving for variable 'y'.

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

Ignore the factor 3.

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

Simplifying
-3 + -4y + y2 = 0

Solving
-3 + -4y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -4y + 3 + y2 = 0 + 3

Reorder the terms:
-3 + 3 + -4y + y2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4y + y2 = 0 + 3
-4y + y2 = 0 + 3

Combine like terms: 0 + 3 = 3
-4y + y2 = 3

The y term is -4y.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4y + 4 + y2 = 3 + 4

Reorder the terms:
4 + -4y + y2 = 3 + 4

Combine like terms: 3 + 4 = 7
4 + -4y + y2 = 7

Factor a perfect square on the left side:
(y + -2)(y + -2) = 7

Calculate the square root of the right side: 2.645751311

Break this problem into two subproblems by setting 
(y + -2) equal to 2.645751311 and -2.645751311.


Subproblem 1
y + -2 = 2.645751311

Simplifying
y + -2 = 2.645751311

Reorder the terms:
-2 + y = 2.645751311

Solving
-2 + y = 2.645751311

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = 2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + y = 2.645751311 + 2
y = 2.645751311 + 2

Combine like terms: 2.645751311 + 2 = 4.645751311
y = 4.645751311

Simplifying
y = 4.645751311


Subproblem 2
y + -2 = -2.645751311

Simplifying
y + -2 = -2.645751311

Reorder the terms:
-2 + y = -2.645751311

Solving
-2 + y = -2.645751311

Solving for variable 'y'.

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

Add '2' to each side of the equation.
-2 + 2 + y = -2.645751311 + 2

Combine like terms: -2 + 2 = 0
0 + y = -2.645751311 + 2
y = -2.645751311 + 2

Combine like terms: -2.645751311 + 2 = -0.645751311
y = -0.645751311

Simplifying
y = -0.645751311


Solution
The solution to the problem is based on the solutions
from the subproblems.
y = {4.645751311, -0.645751311}
Solution
y = {4.645751311, -0.645751311}

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