6y+2(y-5)=6y(y+1)-3

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Solution for 6y+2(y-5)=6y(y+1)-3 equation: 


Simplifying
6y + 2(y + -5) = 6y(y + 1) + -3

Reorder the terms:
6y + 2(-5 + y) = 6y(y + 1) + -3
6y + (-5 * 2 + y * 2) = 6y(y + 1) + -3
6y + (-10 + 2y) = 6y(y + 1) + -3

Reorder the terms:
-10 + 6y + 2y = 6y(y + 1) + -3

Combine like terms: 6y + 2y = 8y
-10 + 8y = 6y(y + 1) + -3

Reorder the terms:
-10 + 8y = 6y(1 + y) + -3
-10 + 8y = (1 * 6y + y * 6y) + -3
-10 + 8y = (6y + 6y2) + -3

Reorder the terms:
-10 + 8y = -3 + 6y + 6y2

Solving
-10 + 8y = -3 + 6y + 6y2

Solving for variable 'y'.

Reorder the terms:
-10 + 3 + 8y + -6y + -6y2 = -3 + 6y + 6y2 + 3 + -6y + -6y2

Combine like terms: -10 + 3 = -7
-7 + 8y + -6y + -6y2 = -3 + 6y + 6y2 + 3 + -6y + -6y2

Combine like terms: 8y + -6y = 2y
-7 + 2y + -6y2 = -3 + 6y + 6y2 + 3 + -6y + -6y2

Reorder the terms:
-7 + 2y + -6y2 = -3 + 3 + 6y + -6y + 6y2 + -6y2

Combine like terms: -3 + 3 = 0
-7 + 2y + -6y2 = 0 + 6y + -6y + 6y2 + -6y2
-7 + 2y + -6y2 = 6y + -6y + 6y2 + -6y2

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

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

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

Divide each side by '-6'.
1.166666667 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -0.3333333333y + -1.166666667 + y2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -0.3333333333y + y2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -0.3333333333y + y2 = 0 + -1.166666667
-0.3333333333y + y2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-0.3333333333y + y2 = -1.166666667

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 = -1.166666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = -1.166666667 + 0.02777777779

Combine like terms: -1.166666667 + 0.02777777779 = -1.13888888921
0.02777777779 + -0.3333333333y + y2 = -1.13888888921

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = -1.13888888921

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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