(8a^2+2a-3)-(-6a^2+4a+7)=0

Solution for (8a^2+2a-3)-(-6a^2+4a+7)=0 equation:

Simplifying
(8a2 + 2a + -3) + -1(-6a2 + 4a + 7) = 0

Reorder the terms:
(-3 + 2a + 8a2) + -1(-6a2 + 4a + 7) = 0

Remove parenthesis around (-3 + 2a + 8a2)
-3 + 2a + 8a2 + -1(-6a2 + 4a + 7) = 0

Reorder the terms:
-3 + 2a + 8a2 + -1(7 + 4a + -6a2) = 0
-3 + 2a + 8a2 + (7 * -1 + 4a * -1 + -6a2 * -1) = 0
-3 + 2a + 8a2 + (-7 + -4a + 6a2) = 0

Reorder the terms:
-3 + -7 + 2a + -4a + 8a2 + 6a2 = 0

Combine like terms: -3 + -7 = -10
-10 + 2a + -4a + 8a2 + 6a2 = 0

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

Combine like terms: 8a2 + 6a2 = 14a2
-10 + -2a + 14a2 = 0

Solving
-10 + -2a + 14a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5 + -1a + 7a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1a + 7a2)' equal to zero and attempt to solve:

Simplifying
-5 + -1a + 7a2 = 0

Solving
-5 + -1a + 7a2 = 0

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

Divide each side by '7'.
-0.7142857143 + -0.1428571429a + a2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -0.1428571429a + 0.7142857143 + a2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -0.1428571429a + a2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -0.1428571429a + a2 = 0 + 0.7142857143
-0.1428571429a + a2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-0.1428571429a + a2 = 0.7142857143

The a term is -0.1428571429a.  Take half its coefficient (-0.07142857145).
Square it (0.005102040819) and add it to both sides.

Add '0.005102040819' to each side of the equation.
-0.1428571429a + 0.005102040819 + a2 = 0.7142857143 + 0.005102040819

Reorder the terms:
0.005102040819 + -0.1428571429a + a2 = 0.7142857143 + 0.005102040819

Combine like terms: 0.7142857143 + 0.005102040819 = 0.719387755119
0.005102040819 + -0.1428571429a + a2 = 0.719387755119

Factor a perfect square on the left side:
(a + -0.07142857145)(a + -0.07142857145) = 0.719387755119

Calculate the square root of the right side: 0.848167292

Break this problem into two subproblems by setting 
(a + -0.07142857145) equal to 0.848167292 and -0.848167292.

Subproblem 1
a + -0.07142857145 = 0.848167292

Simplifying
a + -0.07142857145 = 0.848167292

Reorder the terms:
-0.07142857145 + a = 0.848167292

Solving
-0.07142857145 + a = 0.848167292

Solving for variable 'a'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + a = 0.848167292 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + a = 0.848167292 + 0.07142857145
a = 0.848167292 + 0.07142857145

Combine like terms: 0.848167292 + 0.07142857145 = 0.91959586345
a = 0.91959586345

Simplifying
a = 0.91959586345

Subproblem 2
a + -0.07142857145 = -0.848167292

Simplifying
a + -0.07142857145 = -0.848167292

Reorder the terms:
-0.07142857145 + a = -0.848167292

Solving
-0.07142857145 + a = -0.848167292

Solving for variable 'a'.

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

Add '0.07142857145' to each side of the equation.
-0.07142857145 + 0.07142857145 + a = -0.848167292 + 0.07142857145

Combine like terms: -0.07142857145 + 0.07142857145 = 0.00000000000
0.00000000000 + a = -0.848167292 + 0.07142857145
a = -0.848167292 + 0.07142857145

Combine like terms: -0.848167292 + 0.07142857145 = -0.77673872055
a = -0.77673872055

Simplifying
a = -0.77673872055

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.91959586345, -0.77673872055}
Solution
a = {0.91959586345, -0.77673872055}