3(y^2+3y+4)+4(y^2+3y+2)=

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Solution for 3(y^2+3y+4)+4(y^2+3y+2)= equation: 


Simplifying
3(y2 + 3y + 4) + 4(y2 + 3y + 2) = 0

Reorder the terms:
3(4 + 3y + y2) + 4(y2 + 3y + 2) = 0
(4 * 3 + 3y * 3 + y2 * 3) + 4(y2 + 3y + 2) = 0
(12 + 9y + 3y2) + 4(y2 + 3y + 2) = 0

Reorder the terms:
12 + 9y + 3y2 + 4(2 + 3y + y2) = 0
12 + 9y + 3y2 + (2 * 4 + 3y * 4 + y2 * 4) = 0
12 + 9y + 3y2 + (8 + 12y + 4y2) = 0

Reorder the terms:
12 + 8 + 9y + 12y + 3y2 + 4y2 = 0

Combine like terms: 12 + 8 = 20
20 + 9y + 12y + 3y2 + 4y2 = 0

Combine like terms: 9y + 12y = 21y
20 + 21y + 3y2 + 4y2 = 0

Combine like terms: 3y2 + 4y2 = 7y2
20 + 21y + 7y2 = 0

Solving
20 + 21y + 7y2 = 0

Solving for variable 'y'.

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

Divide each side by '7'.
2.857142857 + 3y + y2 = 0

Move the constant term to the right:

Add '-2.857142857' to each side of the equation.
2.857142857 + 3y + -2.857142857 + y2 = 0 + -2.857142857

Reorder the terms:
2.857142857 + -2.857142857 + 3y + y2 = 0 + -2.857142857

Combine like terms: 2.857142857 + -2.857142857 = 0.000000000
0.000000000 + 3y + y2 = 0 + -2.857142857
3y + y2 = 0 + -2.857142857

Combine like terms: 0 + -2.857142857 = -2.857142857
3y + y2 = -2.857142857

The y term is 3y.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3y + 2.25 + y2 = -2.857142857 + 2.25

Reorder the terms:
2.25 + 3y + y2 = -2.857142857 + 2.25

Combine like terms: -2.857142857 + 2.25 = -0.607142857
2.25 + 3y + y2 = -0.607142857

Factor a perfect square on the left side:
(y + 1.5)(y + 1.5) = -0.607142857

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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