2(y-2)+5(2-y)=-3y(2y+2)

Solution for 2(y-2)+5(2-y)=-3y(2y+2) equation:

Simplifying
2(y + -2) + 5(2 + -1y) = -3y(2y + 2)

Reorder the terms:
2(-2 + y) + 5(2 + -1y) = -3y(2y + 2)
(-2 * 2 + y * 2) + 5(2 + -1y) = -3y(2y + 2)
(-4 + 2y) + 5(2 + -1y) = -3y(2y + 2)
-4 + 2y + (2 * 5 + -1y * 5) = -3y(2y + 2)
-4 + 2y + (10 + -5y) = -3y(2y + 2)

Reorder the terms:
-4 + 10 + 2y + -5y = -3y(2y + 2)

Combine like terms: -4 + 10 = 6
6 + 2y + -5y = -3y(2y + 2)

Combine like terms: 2y + -5y = -3y
6 + -3y = -3y(2y + 2)

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

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

Solving for variable 'y'.

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

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

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

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

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

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

Simplifying
2 + y + 2y2 = 0

Solving
2 + y + 2y2 = 0

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

Divide each side by '2'.
1 + 0.5y + y2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 0.5y + -1 + y2 = 0 + -1

Reorder the terms:
1 + -1 + 0.5y + y2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 0.5y + y2 = 0 + -1
0.5y + y2 = 0 + -1

Combine like terms: 0 + -1 = -1
0.5y + y2 = -1

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 + 0.25

Reorder the terms:
0.25 + 0.5y + y2 = -1 + 0.25

Combine like terms: -1 + 0.25 = -0.75
0.25 + 0.5y + y2 = -0.75

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