3(-2y+3y+1)-3(y^2-2y+4)=

Solution for 3(-2y+3y+1)-3(y^2-2y+4)= equation:

Simplifying
3(-2y + 3y + 1) + -3(y2 + -2y + 4) = 0

Reorder the terms:
3(1 + -2y + 3y) + -3(y2 + -2y + 4) = 0

Combine like terms: -2y + 3y = 1y
3(1 + 1y) + -3(y2 + -2y + 4) = 0
(1 * 3 + 1y * 3) + -3(y2 + -2y + 4) = 0
(3 + 3y) + -3(y2 + -2y + 4) = 0

Reorder the terms:
3 + 3y + -3(4 + -2y + y2) = 0
3 + 3y + (4 * -3 + -2y * -3 + y2 * -3) = 0
3 + 3y + (-12 + 6y + -3y2) = 0

Reorder the terms:
3 + -12 + 3y + 6y + -3y2 = 0

Combine like terms: 3 + -12 = -9
-9 + 3y + 6y + -3y2 = 0

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

Solving
-9 + 9y + -3y2 = 0

Solving for variable 'y'.

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

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

Simplifying
-3 + 3y + -1y2 = 0

Solving
-3 + 3y + -1y2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

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

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -3y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + -3y + y2 = 0 + -3

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

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

The y term is -3y.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3y + 2.25 + y2 = -3 + 2.25

Reorder the terms:
2.25 + -3y + y2 = -3 + 2.25

Combine like terms: -3 + 2.25 = -0.75
2.25 + -3y + y2 = -0.75

Factor a perfect square on the left side:
(y + -1.5)(y + -1.5) = -0.75

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.