y=-3y^2+4y-6

Solution for y=-3y^2+4y-6 equation:

Simplifying
y = -3y2 + 4y + -6

Reorder the terms:
y = -6 + 4y + -3y2

Solving
y = -6 + 4y + -3y2

Solving for variable 'y'.

Reorder the terms:
6 + y + -4y + 3y2 = -6 + 4y + -3y2 + 6 + -4y + 3y2

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

Reorder the terms:
6 + -3y + 3y2 = -6 + 6 + 4y + -4y + -3y2 + 3y2

Combine like terms: -6 + 6 = 0
6 + -3y + 3y2 = 0 + 4y + -4y + -3y2 + 3y2
6 + -3y + 3y2 = 4y + -4y + -3y2 + 3y2

Combine like terms: 4y + -4y = 0
6 + -3y + 3y2 = 0 + -3y2 + 3y2
6 + -3y + 3y2 = -3y2 + 3y2

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

Factor out the Greatest Common Factor (GCF), '3'.
3(2 + -1y + y2) = 0

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

Simplifying
2 + -1y + y2 = 0

Solving
2 + -1y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -1y + -2 + y2 = 0 + -2

Reorder the terms:
2 + -2 + -1y + y2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1y + y2 = 0 + -2
-1y + y2 = 0 + -2

Combine like terms: 0 + -2 = -2
-1y + y2 = -2

The y term is -1y.  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.
-1y + 0.25 + y2 = -2 + 0.25

Reorder the terms:
0.25 + -1y + y2 = -2 + 0.25

Combine like terms: -2 + 0.25 = -1.75
0.25 + -1y + y2 = -1.75

Factor a perfect square on the left side:
(y + -0.5)(y + -0.5) = -1.75

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.