(a^2-4a+6)+(3a^2+13a+6)=

Solution for (a^2-4a+6)+(3a^2+13a+6)= equation:

Simplifying
(a2 + -4a + 6) + (3a2 + 13a + 6) = 0

Reorder the terms:
(6 + -4a + a2) + (3a2 + 13a + 6) = 0

Remove parenthesis around (6 + -4a + a2)
6 + -4a + a2 + (3a2 + 13a + 6) = 0

Reorder the terms:
6 + -4a + a2 + (6 + 13a + 3a2) = 0

Remove parenthesis around (6 + 13a + 3a2)
6 + -4a + a2 + 6 + 13a + 3a2 = 0

Reorder the terms:
6 + 6 + -4a + 13a + a2 + 3a2 = 0

Combine like terms: 6 + 6 = 12
12 + -4a + 13a + a2 + 3a2 = 0

Combine like terms: -4a + 13a = 9a
12 + 9a + a2 + 3a2 = 0

Combine like terms: a2 + 3a2 = 4a2
12 + 9a + 4a2 = 0

Solving
12 + 9a + 4a2 = 0

Solving for variable 'a'.

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

Divide each side by '4'.
3 + 2.25a + a2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 2.25a + -3 + a2 = 0 + -3

Reorder the terms:
3 + -3 + 2.25a + a2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2.25a + a2 = 0 + -3
2.25a + a2 = 0 + -3

Combine like terms: 0 + -3 = -3
2.25a + a2 = -3

The a term is 2.25a.  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.
2.25a + 1.265625 + a2 = -3 + 1.265625

Reorder the terms:
1.265625 + 2.25a + a2 = -3 + 1.265625

Combine like terms: -3 + 1.265625 = -1.734375
1.265625 + 2.25a + a2 = -1.734375

Factor a perfect square on the left side:
(a + 1.125)(a + 1.125) = -1.734375

Can't calculate square root of the right side.

The solution to this equation could not be determined.