2y(3y+4)-6=4y-7

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Solution for 2y(3y+4)-6=4y-7 equation:


Simplifying
2y(3y + 4) + -6 = 4y + -7

Reorder the terms:
2y(4 + 3y) + -6 = 4y + -7
(4 * 2y + 3y * 2y) + -6 = 4y + -7
(8y + 6y2) + -6 = 4y + -7

Reorder the terms:
-6 + 8y + 6y2 = 4y + -7

Reorder the terms:
-6 + 8y + 6y2 = -7 + 4y

Solving
-6 + 8y + 6y2 = -7 + 4y

Solving for variable 'y'.

Reorder the terms:
-6 + 7 + 8y + -4y + 6y2 = -7 + 4y + 7 + -4y

Combine like terms: -6 + 7 = 1
1 + 8y + -4y + 6y2 = -7 + 4y + 7 + -4y

Combine like terms: 8y + -4y = 4y
1 + 4y + 6y2 = -7 + 4y + 7 + -4y

Reorder the terms:
1 + 4y + 6y2 = -7 + 7 + 4y + -4y

Combine like terms: -7 + 7 = 0
1 + 4y + 6y2 = 0 + 4y + -4y
1 + 4y + 6y2 = 4y + -4y

Combine like terms: 4y + -4y = 0
1 + 4y + 6y2 = 0

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

Divide each side by '6'.
0.1666666667 + 0.6666666667y + y2 = 0

Move the constant term to the right:

Add '-0.1666666667' to each side of the equation.
0.1666666667 + 0.6666666667y + -0.1666666667 + y2 = 0 + -0.1666666667

Reorder the terms:
0.1666666667 + -0.1666666667 + 0.6666666667y + y2 = 0 + -0.1666666667

Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000
0.0000000000 + 0.6666666667y + y2 = 0 + -0.1666666667
0.6666666667y + y2 = 0 + -0.1666666667

Combine like terms: 0 + -0.1666666667 = -0.1666666667
0.6666666667y + y2 = -0.1666666667

The y term is 0.6666666667y.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667y + 0.1111111112 + y2 = -0.1666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667y + y2 = -0.1666666667 + 0.1111111112

Combine like terms: -0.1666666667 + 0.1111111112 = -0.0555555555
0.1111111112 + 0.6666666667y + y2 = -0.0555555555

Factor a perfect square on the left side:
(y + 0.3333333334)(y + 0.3333333334) = -0.0555555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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