6y^2-3y=y-6

Solution for 6y^2-3y=y-6 equation:

Simplifying
6y2 + -3y = y + -6

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

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

Solving
-3y + 6y2 = -6 + y

Solving for variable 'y'.

Reorder the terms:
6 + -3y + -1y + 6y2 = -6 + y + 6 + -1y

Combine like terms: -3y + -1y = -4y
6 + -4y + 6y2 = -6 + y + 6 + -1y

Reorder the terms:
6 + -4y + 6y2 = -6 + 6 + y + -1y

Combine like terms: -6 + 6 = 0
6 + -4y + 6y2 = 0 + y + -1y
6 + -4y + 6y2 = y + -1y

Combine like terms: y + -1y = 0
6 + -4y + 6y2 = 0

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

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

Simplifying
3 + -2y + 3y2 = 0

Solving
3 + -2y + 3y2 = 0

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

Divide each side by '3'.
1 + -0.6666666667y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -0.6666666667y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + -0.6666666667y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -0.6666666667y + y2 = 0 + -1
-0.6666666667y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
-0.6666666667y + y2 = -1

The y term is -0.6666666667y.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667y + 0.1111111112 + y2 = -1 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667y + y2 = -1 + 0.1111111112

Combine like terms: -1 + 0.1111111112 = -0.8888888888
0.1111111112 + -0.6666666667y + y2 = -0.8888888888

Factor a perfect square on the left side:
(y + -0.3333333334)(y + -0.3333333334) = -0.8888888888

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.