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

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

Simplifying
3a2 + -7a + 6 + -4a2 + -3a + a = 0

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

Combine like terms: -7a + -3a = -10a
6 + -10a + a + 3a2 + -4a2 = 0

Combine like terms: -10a + a = -9a
6 + -9a + 3a2 + -4a2 = 0

Combine like terms: 3a2 + -4a2 = -1a2
6 + -9a + -1a2 = 0

Solving
6 + -9a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 9a + a2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 9a + 6 + a2 = 0 + 6

Reorder the terms:
-6 + 6 + 9a + a2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 9a + a2 = 0 + 6
9a + a2 = 0 + 6

Combine like terms: 0 + 6 = 6
9a + a2 = 6

The a term is 9a.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9a + 20.25 + a2 = 6 + 20.25

Reorder the terms:
20.25 + 9a + a2 = 6 + 20.25

Combine like terms: 6 + 20.25 = 26.25
20.25 + 9a + a2 = 26.25

Factor a perfect square on the left side:
(a + 4.5)(a + 4.5) = 26.25

Calculate the square root of the right side: 5.123475383

Break this problem into two subproblems by setting 
(a + 4.5) equal to 5.123475383 and -5.123475383.

Subproblem 1
a + 4.5 = 5.123475383

Simplifying
a + 4.5 = 5.123475383

Reorder the terms:
4.5 + a = 5.123475383

Solving
4.5 + a = 5.123475383

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = 5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = 5.123475383 + -4.5
a = 5.123475383 + -4.5

Combine like terms: 5.123475383 + -4.5 = 0.623475383
a = 0.623475383

Simplifying
a = 0.623475383

Subproblem 2
a + 4.5 = -5.123475383

Simplifying
a + 4.5 = -5.123475383

Reorder the terms:
4.5 + a = -5.123475383

Solving
4.5 + a = -5.123475383

Solving for variable 'a'.

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

Add '-4.5' to each side of the equation.
4.5 + -4.5 + a = -5.123475383 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + a = -5.123475383 + -4.5
a = -5.123475383 + -4.5

Combine like terms: -5.123475383 + -4.5 = -9.623475383
a = -9.623475383

Simplifying
a = -9.623475383

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.623475383, -9.623475383}