(-a^2+3)-(a^2-1)+(4a^2-5a+6)=

Solution for (-a^2+3)-(a^2-1)+(4a^2-5a+6)= equation:

Simplifying
(-1a2 + 3) + -1(a2 + -1) + (4a2 + -5a + 6) = 0

Reorder the terms:
(3 + -1a2) + -1(a2 + -1) + (4a2 + -5a + 6) = 0

Remove parenthesis around (3 + -1a2)
3 + -1a2 + -1(a2 + -1) + (4a2 + -5a + 6) = 0

Reorder the terms:
3 + -1a2 + -1(-1 + a2) + (4a2 + -5a + 6) = 0
3 + -1a2 + (-1 * -1 + a2 * -1) + (4a2 + -5a + 6) = 0
3 + -1a2 + (1 + -1a2) + (4a2 + -5a + 6) = 0

Reorder the terms:
3 + -1a2 + 1 + -1a2 + (6 + -5a + 4a2) = 0

Remove parenthesis around (6 + -5a + 4a2)
3 + -1a2 + 1 + -1a2 + 6 + -5a + 4a2 = 0

Reorder the terms:
3 + 1 + 6 + -5a + -1a2 + -1a2 + 4a2 = 0

Combine like terms: 3 + 1 = 4
4 + 6 + -5a + -1a2 + -1a2 + 4a2 = 0

Combine like terms: 4 + 6 = 10
10 + -5a + -1a2 + -1a2 + 4a2 = 0

Combine like terms: -1a2 + -1a2 = -2a2
10 + -5a + -2a2 + 4a2 = 0

Combine like terms: -2a2 + 4a2 = 2a2
10 + -5a + 2a2 = 0

Solving
10 + -5a + 2a2 = 0

Solving for variable 'a'.

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

Divide each side by '2'.
5 + -2.5a + a2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -2.5a + -5 + a2 = 0 + -5

Reorder the terms:
5 + -5 + -2.5a + a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2.5a + a2 = 0 + -5
-2.5a + a2 = 0 + -5

Combine like terms: 0 + -5 = -5
-2.5a + a2 = -5

The a term is -2.5a.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5a + 1.5625 + a2 = -5 + 1.5625

Reorder the terms:
1.5625 + -2.5a + a2 = -5 + 1.5625

Combine like terms: -5 + 1.5625 = -3.4375
1.5625 + -2.5a + a2 = -3.4375

Factor a perfect square on the left side:
(a + -1.25)(a + -1.25) = -3.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.