-4y+10=-2y(3y+1)

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Solution for -4y+10=-2y(3y+1) equation: 


Simplifying
-4y + 10 = -2y(3y + 1)

Reorder the terms:
10 + -4y = -2y(3y + 1)

Reorder the terms:
10 + -4y = -2y(1 + 3y)
10 + -4y = (1 * -2y + 3y * -2y)
10 + -4y = (-2y + -6y2)

Solving
10 + -4y = -2y + -6y2

Solving for variable 'y'.

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

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

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -1y + 3y2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + -1y + 3y2)' equal to zero and attempt to solve:

Simplifying
5 + -1y + 3y2 = 0

Solving
5 + -1y + 3y2 = 0

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

Divide each side by '3'.
1.666666667 + -0.3333333333y + y2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -0.3333333333y + -1.666666667 + y2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -0.3333333333y + y2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -0.3333333333y + y2 = 0 + -1.666666667
-0.3333333333y + y2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-0.3333333333y + y2 = -1.666666667

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 = -1.666666667 + 0.02777777779

Reorder the terms:
0.02777777779 + -0.3333333333y + y2 = -1.666666667 + 0.02777777779

Combine like terms: -1.666666667 + 0.02777777779 = -1.63888888921
0.02777777779 + -0.3333333333y + y2 = -1.63888888921

Factor a perfect square on the left side:
(y + -0.1666666667)(y + -0.1666666667) = -1.63888888921

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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