6y(y+2)-3y+4=6y+y-5

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Solution for 6y(y+2)-3y+4=6y+y-5 equation: 


Simplifying
6y(y + 2) + -3y + 4 = 6y + y + -5

Reorder the terms:
6y(2 + y) + -3y + 4 = 6y + y + -5
(2 * 6y + y * 6y) + -3y + 4 = 6y + y + -5
(12y + 6y2) + -3y + 4 = 6y + y + -5

Reorder the terms:
4 + 12y + -3y + 6y2 = 6y + y + -5

Combine like terms: 12y + -3y = 9y
4 + 9y + 6y2 = 6y + y + -5

Reorder the terms:
4 + 9y + 6y2 = -5 + 6y + y

Combine like terms: 6y + y = 7y
4 + 9y + 6y2 = -5 + 7y

Solving
4 + 9y + 6y2 = -5 + 7y

Solving for variable 'y'.

Reorder the terms:
4 + 5 + 9y + -7y + 6y2 = -5 + 7y + 5 + -7y

Combine like terms: 4 + 5 = 9
9 + 9y + -7y + 6y2 = -5 + 7y + 5 + -7y

Combine like terms: 9y + -7y = 2y
9 + 2y + 6y2 = -5 + 7y + 5 + -7y

Reorder the terms:
9 + 2y + 6y2 = -5 + 5 + 7y + -7y

Combine like terms: -5 + 5 = 0
9 + 2y + 6y2 = 0 + 7y + -7y
9 + 2y + 6y2 = 7y + -7y

Combine like terms: 7y + -7y = 0
9 + 2y + 6y2 = 0

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

Divide each side by '6'.
1.5 + 0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + 0.3333333333y + -1.5 + y2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + 0.3333333333y + y2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + 0.3333333333y + y2 = 0 + -1.5
0.3333333333y + y2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
0.3333333333y + y2 = -1.5

The y term is 0.3333333333y.  Take half its coefficient (0.1666666667).
Square it (0.02777777779) and add it to both sides.

Add '0.02777777779' to each side of the equation.
0.3333333333y + 0.02777777779 + y2 = -1.5 + 0.02777777779

Reorder the terms:
0.02777777779 + 0.3333333333y + y2 = -1.5 + 0.02777777779

Combine like terms: -1.5 + 0.02777777779 = -1.47222222221
0.02777777779 + 0.3333333333y + y2 = -1.47222222221

Factor a perfect square on the left side:
(y + 0.1666666667)(y + 0.1666666667) = -1.47222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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