(4y^2+7y+1)-(y^2-12)=

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Solution for (4y^2+7y+1)-(y^2-12)= equation: 


Simplifying
(4y2 + 7y + 1) + -1(y2 + -12) = 0

Reorder the terms:
(1 + 7y + 4y2) + -1(y2 + -12) = 0

Remove parenthesis around (1 + 7y + 4y2)
1 + 7y + 4y2 + -1(y2 + -12) = 0

Reorder the terms:
1 + 7y + 4y2 + -1(-12 + y2) = 0
1 + 7y + 4y2 + (-12 * -1 + y2 * -1) = 0
1 + 7y + 4y2 + (12 + -1y2) = 0

Reorder the terms:
1 + 12 + 7y + 4y2 + -1y2 = 0

Combine like terms: 1 + 12 = 13
13 + 7y + 4y2 + -1y2 = 0

Combine like terms: 4y2 + -1y2 = 3y2
13 + 7y + 3y2 = 0

Solving
13 + 7y + 3y2 = 0

Solving for variable 'y'.

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

Divide each side by '3'.
4.333333333 + 2.333333333y + y2 = 0

Move the constant term to the right:

Add '-4.333333333' to each side of the equation.
4.333333333 + 2.333333333y + -4.333333333 + y2 = 0 + -4.333333333

Reorder the terms:
4.333333333 + -4.333333333 + 2.333333333y + y2 = 0 + -4.333333333

Combine like terms: 4.333333333 + -4.333333333 = 0.000000000
0.000000000 + 2.333333333y + y2 = 0 + -4.333333333
2.333333333y + y2 = 0 + -4.333333333

Combine like terms: 0 + -4.333333333 = -4.333333333
2.333333333y + y2 = -4.333333333

The y term is 2.333333333y.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333y + 1.361111112 + y2 = -4.333333333 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333y + y2 = -4.333333333 + 1.361111112

Combine like terms: -4.333333333 + 1.361111112 = -2.972222221
1.361111112 + 2.333333333y + y2 = -2.972222221

Factor a perfect square on the left side:
(y + 1.166666667)(y + 1.166666667) = -2.972222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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