4y^2-6y=-6

Solution for 4y^2-6y=-6 equation:

Simplifying
4y2 + -6y = -6

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

Solving
-6y + 4y2 = -6

Solving for variable 'y'.

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

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

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

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

Simplifying
3 + -3y + 2y2 = 0

Solving
3 + -3y + 2y2 = 0

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

Divide each side by '2'.
1.5 + -1.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -1.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -1.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -1.5y + y2 = 0 + -1.5
-1.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-1.5y + y2 = -1.5

The y term is -1.5y.  Take half its coefficient (-0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
-1.5y + 0.5625 + y2 = -1.5 + 0.5625

Reorder the terms:
0.5625 + -1.5y + y2 = -1.5 + 0.5625

Combine like terms: -1.5 + 0.5625 = -0.9375
0.5625 + -1.5y + y2 = -0.9375

Factor a perfect square on the left side:
(y + -0.75)(y + -0.75) = -0.9375

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.