4y-6=-2y(-2y-1)

Solution for 4y-6=-2y(-2y-1) equation:

Simplifying
4y + -6 = -2y(-2y + -1)

Reorder the terms:
-6 + 4y = -2y(-2y + -1)

Reorder the terms:
-6 + 4y = -2y(-1 + -2y)
-6 + 4y = (-1 * -2y + -2y * -2y)
-6 + 4y = (2y + 4y2)

Solving
-6 + 4y = 2y + 4y2

Solving for variable 'y'.

Combine like terms: 4y + -2y = 2y
-6 + 2y + -4y2 = 2y + 4y2 + -2y + -4y2

Reorder the terms:
-6 + 2y + -4y2 = 2y + -2y + 4y2 + -4y2

Combine like terms: 2y + -2y = 0
-6 + 2y + -4y2 = 0 + 4y2 + -4y2
-6 + 2y + -4y2 = 4y2 + -4y2

Combine like terms: 4y2 + -4y2 = 0
-6 + 2y + -4y2 = 0

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

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

Simplifying
-3 + y + -2y2 = 0

Solving
-3 + y + -2y2 = 0

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

Divide each side by '-2'.
1.5 + -0.5y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + -0.5y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + -0.5y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + -0.5y + y2 = 0 + -1.5
-0.5y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
-0.5y + y2 = -1.5

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.
-0.5y + 0.25 + y2 = -1.5 + 0.25

Reorder the terms:
0.25 + -0.5y + y2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
0.25 + -0.5y + y2 = -1.25

Factor a perfect square on the left side:
(y + 0.5)(y + 0.5) = -1.25

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.