5y+3(y-5)=6y(y+1)-4

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Solution for 5y+3(y-5)=6y(y+1)-4 equation: 


Simplifying
5y + 3(y + -5) = 6y(y + 1) + -4

Reorder the terms:
5y + 3(-5 + y) = 6y(y + 1) + -4
5y + (-5 * 3 + y * 3) = 6y(y + 1) + -4
5y + (-15 + 3y) = 6y(y + 1) + -4

Reorder the terms:
-15 + 5y + 3y = 6y(y + 1) + -4

Combine like terms: 5y + 3y = 8y
-15 + 8y = 6y(y + 1) + -4

Reorder the terms:
-15 + 8y = 6y(1 + y) + -4
-15 + 8y = (1 * 6y + y * 6y) + -4
-15 + 8y = (6y + 6y2) + -4

Reorder the terms:
-15 + 8y = -4 + 6y + 6y2

Solving
-15 + 8y = -4 + 6y + 6y2

Solving for variable 'y'.

Reorder the terms:
-15 + 4 + 8y + -6y + -6y2 = -4 + 6y + 6y2 + 4 + -6y + -6y2

Combine like terms: -15 + 4 = -11
-11 + 8y + -6y + -6y2 = -4 + 6y + 6y2 + 4 + -6y + -6y2

Combine like terms: 8y + -6y = 2y
-11 + 2y + -6y2 = -4 + 6y + 6y2 + 4 + -6y + -6y2

Reorder the terms:
-11 + 2y + -6y2 = -4 + 4 + 6y + -6y + 6y2 + -6y2

Combine like terms: -4 + 4 = 0
-11 + 2y + -6y2 = 0 + 6y + -6y + 6y2 + -6y2
-11 + 2y + -6y2 = 6y + -6y + 6y2 + -6y2

Combine like terms: 6y + -6y = 0
-11 + 2y + -6y2 = 0 + 6y2 + -6y2
-11 + 2y + -6y2 = 6y2 + -6y2

Combine like terms: 6y2 + -6y2 = 0
-11 + 2y + -6y2 = 0

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

Divide each side by '-6'.
1.833333333 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-1.833333333' to each side of the equation.
1.833333333 + -0.3333333333y + -1.833333333 + y2 = 0 + -1.833333333

Reorder the terms:
1.833333333 + -1.833333333 + -0.3333333333y + y2 = 0 + -1.833333333

Combine like terms: 1.833333333 + -1.833333333 = 0.000000000
0.000000000 + -0.3333333333y + y2 = 0 + -1.833333333
-0.3333333333y + y2 = 0 + -1.833333333

Combine like terms: 0 + -1.833333333 = -1.833333333
-0.3333333333y + y2 = -1.833333333

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 = -1.833333333 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = -1.833333333 + 0.02777777779

Combine like terms: -1.833333333 + 0.02777777779 = -1.80555555521
0.02777777779 + -0.3333333333y + y2 = -1.80555555521

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = -1.80555555521

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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