-3y(3y+1)=6

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Solution for -3y(3y+1)=6 equation: 


Simplifying
-3y(3y + 1) = 6

Reorder the terms:
-3y(1 + 3y) = 6
(1 * -3y + 3y * -3y) = 6
(-3y + -9y2) = 6

Solving
-3y + -9y2 = 6

Solving for variable 'y'.

Reorder the terms:
-6 + -3y + -9y2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -3y + -9y2 = 0

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

Ignore the factor -3.

Subproblem 1
Set the factor '(2 + y + 3y2)' equal to zero and attempt to solve:

Simplifying
2 + y + 3y2 = 0

Solving
2 + y + 3y2 = 0

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

Divide each side by '3'.
0.6666666667 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 0.3333333333y + -0.6666666667 + y2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 0.3333333333y + y2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 0.3333333333y + y2 = 0 + -0.6666666667
0.3333333333y + y2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
0.3333333333y + y2 = -0.6666666667

The y term is y.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333y + 0.25 + y2 = -0.6666666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333y + y2 = -0.6666666667 + 0.25

Combine like terms: -0.6666666667 + 0.25 = -0.4166666667
0.25 + 0.3333333333y + y2 = -0.4166666667

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -0.4166666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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