y^2-4y-2=2y^2+6y+28

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Solution for y^2-4y-2=2y^2+6y+28 equation: 


Simplifying
y2 + -4y + -2 = 2y2 + 6y + 28

Reorder the terms:
-2 + -4y + y2 = 2y2 + 6y + 28

Reorder the terms:
-2 + -4y + y2 = 28 + 6y + 2y2

Solving
-2 + -4y + y2 = 28 + 6y + 2y2

Solving for variable 'y'.

Reorder the terms:
-2 + -28 + -4y + -6y + y2 + -2y2 = 28 + 6y + 2y2 + -28 + -6y + -2y2

Combine like terms: -2 + -28 = -30
-30 + -4y + -6y + y2 + -2y2 = 28 + 6y + 2y2 + -28 + -6y + -2y2

Combine like terms: -4y + -6y = -10y
-30 + -10y + y2 + -2y2 = 28 + 6y + 2y2 + -28 + -6y + -2y2

Combine like terms: y2 + -2y2 = -1y2
-30 + -10y + -1y2 = 28 + 6y + 2y2 + -28 + -6y + -2y2

Reorder the terms:
-30 + -10y + -1y2 = 28 + -28 + 6y + -6y + 2y2 + -2y2

Combine like terms: 28 + -28 = 0
-30 + -10y + -1y2 = 0 + 6y + -6y + 2y2 + -2y2
-30 + -10y + -1y2 = 6y + -6y + 2y2 + -2y2

Combine like terms: 6y + -6y = 0
-30 + -10y + -1y2 = 0 + 2y2 + -2y2
-30 + -10y + -1y2 = 2y2 + -2y2

Combine like terms: 2y2 + -2y2 = 0
-30 + -10y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(30 + 10y + y2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(30 + 10y + y2)' equal to zero and attempt to solve:

Simplifying
30 + 10y + y2 = 0

Solving
30 + 10y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-30' to each side of the equation.
30 + 10y + -30 + y2 = 0 + -30

Reorder the terms:
30 + -30 + 10y + y2 = 0 + -30

Combine like terms: 30 + -30 = 0
0 + 10y + y2 = 0 + -30
10y + y2 = 0 + -30

Combine like terms: 0 + -30 = -30
10y + y2 = -30

The y term is 10y.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10y + 25 + y2 = -30 + 25

Reorder the terms:
25 + 10y + y2 = -30 + 25

Combine like terms: -30 + 25 = -5
25 + 10y + y2 = -5

Factor a perfect square on the left side:
(y + 5)(y + 5) = -5

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.

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