2y^2+10y=6y-6

Solution for 2y^2+10y=6y-6 equation:

Simplifying
2y2 + 10y = 6y + -6

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

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

Solving
10y + 2y2 = -6 + 6y

Solving for variable 'y'.

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

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

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

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

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

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

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

Simplifying
3 + 2y + y2 = 0

Solving
3 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2y + -3 + y2 = 0 + -3

Reorder the terms:
3 + -3 + 2y + y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y + y2 = 0 + -3
2y + y2 = 0 + -3

Combine like terms: 0 + -3 = -3
2y + y2 = -3

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 = -3 + 1

Reorder the terms:
1 + 2y + y2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + 2y + y2 = -2

Factor a perfect square on the left side:
(y + 1)(y + 1) = -2

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.