(-4a^2+2a+10)+(5a^2-10a-12)+(-8a^2-5a+6)=

Solution for (-4a^2+2a+10)+(5a^2-10a-12)+(-8a^2-5a+6)= equation:

Simplifying
(-4a2 + 2a + 10) + (5a2 + -10a + -12) + (-8a2 + -5a + 6) = 0

Reorder the terms:
(10 + 2a + -4a2) + (5a2 + -10a + -12) + (-8a2 + -5a + 6) = 0

Remove parenthesis around (10 + 2a + -4a2)
10 + 2a + -4a2 + (5a2 + -10a + -12) + (-8a2 + -5a + 6) = 0

Reorder the terms:
10 + 2a + -4a2 + (-12 + -10a + 5a2) + (-8a2 + -5a + 6) = 0

Remove parenthesis around (-12 + -10a + 5a2)
10 + 2a + -4a2 + -12 + -10a + 5a2 + (-8a2 + -5a + 6) = 0

Reorder the terms:
10 + 2a + -4a2 + -12 + -10a + 5a2 + (6 + -5a + -8a2) = 0

Remove parenthesis around (6 + -5a + -8a2)
10 + 2a + -4a2 + -12 + -10a + 5a2 + 6 + -5a + -8a2 = 0

Reorder the terms:
10 + -12 + 6 + 2a + -10a + -5a + -4a2 + 5a2 + -8a2 = 0

Combine like terms: 10 + -12 = -2
-2 + 6 + 2a + -10a + -5a + -4a2 + 5a2 + -8a2 = 0

Combine like terms: -2 + 6 = 4
4 + 2a + -10a + -5a + -4a2 + 5a2 + -8a2 = 0

Combine like terms: 2a + -10a = -8a
4 + -8a + -5a + -4a2 + 5a2 + -8a2 = 0

Combine like terms: -8a + -5a = -13a
4 + -13a + -4a2 + 5a2 + -8a2 = 0

Combine like terms: -4a2 + 5a2 = 1a2
4 + -13a + 1a2 + -8a2 = 0

Combine like terms: 1a2 + -8a2 = -7a2
4 + -13a + -7a2 = 0

Solving
4 + -13a + -7a2 = 0

Solving for variable 'a'.

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

Divide each side by '-7'.
-0.5714285714 + 1.857142857a + a2 = 0

Move the constant term to the right:

Add '0.5714285714' to each side of the equation.
-0.5714285714 + 1.857142857a + 0.5714285714 + a2 = 0 + 0.5714285714

Reorder the terms:
-0.5714285714 + 0.5714285714 + 1.857142857a + a2 = 0 + 0.5714285714

Combine like terms: -0.5714285714 + 0.5714285714 = 0.0000000000
0.0000000000 + 1.857142857a + a2 = 0 + 0.5714285714
1.857142857a + a2 = 0 + 0.5714285714

Combine like terms: 0 + 0.5714285714 = 0.5714285714
1.857142857a + a2 = 0.5714285714

The a term is 1.857142857a.  Take half its coefficient (0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
1.857142857a + 0.8622448978 + a2 = 0.5714285714 + 0.8622448978

Reorder the terms:
0.8622448978 + 1.857142857a + a2 = 0.5714285714 + 0.8622448978

Combine like terms: 0.5714285714 + 0.8622448978 = 1.4336734692
0.8622448978 + 1.857142857a + a2 = 1.4336734692

Factor a perfect square on the left side:
(a + 0.9285714285)(a + 0.9285714285) = 1.4336734692

Calculate the square root of the right side: 1.197361044

Break this problem into two subproblems by setting 
(a + 0.9285714285) equal to 1.197361044 and -1.197361044.

Subproblem 1
a + 0.9285714285 = 1.197361044

Simplifying
a + 0.9285714285 = 1.197361044

Reorder the terms:
0.9285714285 + a = 1.197361044

Solving
0.9285714285 + a = 1.197361044

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + a = 1.197361044 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + a = 1.197361044 + -0.9285714285
a = 1.197361044 + -0.9285714285

Combine like terms: 1.197361044 + -0.9285714285 = 0.2687896155
a = 0.2687896155

Simplifying
a = 0.2687896155

Subproblem 2
a + 0.9285714285 = -1.197361044

Simplifying
a + 0.9285714285 = -1.197361044

Reorder the terms:
0.9285714285 + a = -1.197361044

Solving
0.9285714285 + a = -1.197361044

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-0.9285714285' to each side of the equation.
0.9285714285 + -0.9285714285 + a = -1.197361044 + -0.9285714285

Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000
0.0000000000 + a = -1.197361044 + -0.9285714285
a = -1.197361044 + -0.9285714285

Combine like terms: -1.197361044 + -0.9285714285 = -2.1259324725
a = -2.1259324725

Simplifying
a = -2.1259324725

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.2687896155, -2.1259324725}