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

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


Simplifying
(7y2 + 7) + (7y + 2) + -1(3y2 + -2y + -6) = 0

Reorder the terms:
(7 + 7y2) + (7y + 2) + -1(3y2 + -2y + -6) = 0

Remove parenthesis around (7 + 7y2)
7 + 7y2 + (7y + 2) + -1(3y2 + -2y + -6) = 0

Reorder the terms:
7 + 7y2 + (2 + 7y) + -1(3y2 + -2y + -6) = 0

Remove parenthesis around (2 + 7y)
7 + 7y2 + 2 + 7y + -1(3y2 + -2y + -6) = 0

Reorder the terms:
7 + 7y2 + 2 + 7y + -1(-6 + -2y + 3y2) = 0
7 + 7y2 + 2 + 7y + (-6 * -1 + -2y * -1 + 3y2 * -1) = 0
7 + 7y2 + 2 + 7y + (6 + 2y + -3y2) = 0

Reorder the terms:
7 + 2 + 6 + 7y + 2y + 7y2 + -3y2 = 0

Combine like terms: 7 + 2 = 9
9 + 6 + 7y + 2y + 7y2 + -3y2 = 0

Combine like terms: 9 + 6 = 15
15 + 7y + 2y + 7y2 + -3y2 = 0

Combine like terms: 7y + 2y = 9y
15 + 9y + 7y2 + -3y2 = 0

Combine like terms: 7y2 + -3y2 = 4y2
15 + 9y + 4y2 = 0

Solving
15 + 9y + 4y2 = 0

Solving for variable 'y'.

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

Divide each side by '4'.
3.75 + 2.25y + y2 = 0

Move the constant term to the right:

Add '-3.75' to each side of the equation.
3.75 + 2.25y + -3.75 + y2 = 0 + -3.75

Reorder the terms:
3.75 + -3.75 + 2.25y + y2 = 0 + -3.75

Combine like terms: 3.75 + -3.75 = 0.00
0.00 + 2.25y + y2 = 0 + -3.75
2.25y + y2 = 0 + -3.75

Combine like terms: 0 + -3.75 = -3.75
2.25y + y2 = -3.75

The y term is 2.25y.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25y + 1.265625 + y2 = -3.75 + 1.265625

Reorder the terms:
1.265625 + 2.25y + y2 = -3.75 + 1.265625

Combine like terms: -3.75 + 1.265625 = -2.484375
1.265625 + 2.25y + y2 = -2.484375

Factor a perfect square on the left side:
(y + 1.125)(y + 1.125) = -2.484375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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