(-a^2+3)-(a^2-4)+(7a^2-4a+6)=

Solution for (-a^2+3)-(a^2-4)+(7a^2-4a+6)= equation:

Simplifying
(-1a2 + 3) + -1(a2 + -4) + (7a2 + -4a + 6) = 0

Reorder the terms:
(3 + -1a2) + -1(a2 + -4) + (7a2 + -4a + 6) = 0

Remove parenthesis around (3 + -1a2)
3 + -1a2 + -1(a2 + -4) + (7a2 + -4a + 6) = 0

Reorder the terms:
3 + -1a2 + -1(-4 + a2) + (7a2 + -4a + 6) = 0
3 + -1a2 + (-4 * -1 + a2 * -1) + (7a2 + -4a + 6) = 0
3 + -1a2 + (4 + -1a2) + (7a2 + -4a + 6) = 0

Reorder the terms:
3 + -1a2 + 4 + -1a2 + (6 + -4a + 7a2) = 0

Remove parenthesis around (6 + -4a + 7a2)
3 + -1a2 + 4 + -1a2 + 6 + -4a + 7a2 = 0

Reorder the terms:
3 + 4 + 6 + -4a + -1a2 + -1a2 + 7a2 = 0

Combine like terms: 3 + 4 = 7
7 + 6 + -4a + -1a2 + -1a2 + 7a2 = 0

Combine like terms: 7 + 6 = 13
13 + -4a + -1a2 + -1a2 + 7a2 = 0

Combine like terms: -1a2 + -1a2 = -2a2
13 + -4a + -2a2 + 7a2 = 0

Combine like terms: -2a2 + 7a2 = 5a2
13 + -4a + 5a2 = 0

Solving
13 + -4a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
2.6 + -0.8a + a2 = 0

Move the constant term to the right:

Add '-2.6' to each side of the equation.
2.6 + -0.8a + -2.6 + a2 = 0 + -2.6

Reorder the terms:
2.6 + -2.6 + -0.8a + a2 = 0 + -2.6

Combine like terms: 2.6 + -2.6 = 0.0
0.0 + -0.8a + a2 = 0 + -2.6
-0.8a + a2 = 0 + -2.6

Combine like terms: 0 + -2.6 = -2.6
-0.8a + a2 = -2.6

The a term is -0.8a.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8a + 0.16 + a2 = -2.6 + 0.16

Reorder the terms:
0.16 + -0.8a + a2 = -2.6 + 0.16

Combine like terms: -2.6 + 0.16 = -2.44
0.16 + -0.8a + a2 = -2.44

Factor a perfect square on the left side:
(a + -0.4)(a + -0.4) = -2.44

Can't calculate square root of the right side.

The solution to this equation could not be determined.