(6y^2-9y+1)-(-3y^2+3y+1)+(-3y^2+7y+7)=

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Solution for (6y^2-9y+1)-(-3y^2+3y+1)+(-3y^2+7y+7)= equation:


Simplifying
(6y2 + -9y + 1) + -1(-3y2 + 3y + 1) + (-3y2 + 7y + 7) = 0

Reorder the terms:
(1 + -9y + 6y2) + -1(-3y2 + 3y + 1) + (-3y2 + 7y + 7) = 0

Remove parenthesis around (1 + -9y + 6y2)
1 + -9y + 6y2 + -1(-3y2 + 3y + 1) + (-3y2 + 7y + 7) = 0

Reorder the terms:
1 + -9y + 6y2 + -1(1 + 3y + -3y2) + (-3y2 + 7y + 7) = 0
1 + -9y + 6y2 + (1 * -1 + 3y * -1 + -3y2 * -1) + (-3y2 + 7y + 7) = 0
1 + -9y + 6y2 + (-1 + -3y + 3y2) + (-3y2 + 7y + 7) = 0

Reorder the terms:
1 + -9y + 6y2 + -1 + -3y + 3y2 + (7 + 7y + -3y2) = 0

Remove parenthesis around (7 + 7y + -3y2)
1 + -9y + 6y2 + -1 + -3y + 3y2 + 7 + 7y + -3y2 = 0

Reorder the terms:
1 + -1 + 7 + -9y + -3y + 7y + 6y2 + 3y2 + -3y2 = 0

Combine like terms: 1 + -1 = 0
0 + 7 + -9y + -3y + 7y + 6y2 + 3y2 + -3y2 = 0
7 + -9y + -3y + 7y + 6y2 + 3y2 + -3y2 = 0

Combine like terms: -9y + -3y = -12y
7 + -12y + 7y + 6y2 + 3y2 + -3y2 = 0

Combine like terms: -12y + 7y = -5y
7 + -5y + 6y2 + 3y2 + -3y2 = 0

Combine like terms: 6y2 + 3y2 = 9y2
7 + -5y + 9y2 + -3y2 = 0

Combine like terms: 9y2 + -3y2 = 6y2
7 + -5y + 6y2 = 0

Solving
7 + -5y + 6y2 = 0

Solving for variable 'y'.

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

Divide each side by '6'.
1.166666667 + -0.8333333333y + y2 = 0

Move the constant term to the right:

Add '-1.166666667' to each side of the equation.
1.166666667 + -0.8333333333y + -1.166666667 + y2 = 0 + -1.166666667

Reorder the terms:
1.166666667 + -1.166666667 + -0.8333333333y + y2 = 0 + -1.166666667

Combine like terms: 1.166666667 + -1.166666667 = 0.000000000
0.000000000 + -0.8333333333y + y2 = 0 + -1.166666667
-0.8333333333y + y2 = 0 + -1.166666667

Combine like terms: 0 + -1.166666667 = -1.166666667
-0.8333333333y + y2 = -1.166666667

The y term is -0.8333333333y.  Take half its coefficient (-0.4166666667).
Square it (0.1736111111) and add it to both sides.

Add '0.1736111111' to each side of the equation.
-0.8333333333y + 0.1736111111 + y2 = -1.166666667 + 0.1736111111

Reorder the terms:
0.1736111111 + -0.8333333333y + y2 = -1.166666667 + 0.1736111111

Combine like terms: -1.166666667 + 0.1736111111 = -0.9930555559
0.1736111111 + -0.8333333333y + y2 = -0.9930555559

Factor a perfect square on the left side:
(y + -0.4166666667)(y + -0.4166666667) = -0.9930555559

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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