2y(y-1)+6y=-10

Solution for 2y(y-1)+6y=-10 equation:

Simplifying
2y(y + -1) + 6y = -10

Reorder the terms:
2y(-1 + y) + 6y = -10
(-1 * 2y + y * 2y) + 6y = -10
(-2y + 2y2) + 6y = -10

Reorder the terms:
-2y + 6y + 2y2 = -10

Combine like terms: -2y + 6y = 4y
4y + 2y2 = -10

Solving
4y + 2y2 = -10

Solving for variable 'y'.

Reorder the terms:
10 + 4y + 2y2 = -10 + 10

Combine like terms: -10 + 10 = 0
10 + 4y + 2y2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 2y + y2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(5 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
5 + 2y + y2 = 0

Solving
5 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 2y + -5 + y2 = 0 + -5

Reorder the terms:
5 + -5 + 2y + y2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2y + y2 = 0 + -5
2y + y2 = 0 + -5

Combine like terms: 0 + -5 = -5
2y + y2 = -5

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -5 + 1

Reorder the terms:
1 + 2y + y2 = -5 + 1

Combine like terms: -5 + 1 = -4
1 + 2y + y2 = -4

Factor a perfect square on the left side:
(y + 1)(y + 1) = -4

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.