8x^2+6x-12=0

Solution for 8x^2+6x-12=0 equation:

Simplifying
8x2 + 6x + -12 = 0

Reorder the terms:
-12 + 6x + 8x2 = 0

Solving
-12 + 6x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 3x + 4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + 3x + 4x2)' equal to zero and attempt to solve:

Simplifying
-6 + 3x + 4x2 = 0

Solving
-6 + 3x + 4x2 = 0

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

Divide each side by '4'.
-1.5 + 0.75x + x2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.75x + 1.5 + x2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.75x + x2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.75x + x2 = 0 + 1.5
0.75x + x2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
0.75x + x2 = 1.5

The x term is 0.75x.  Take half its coefficient (0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
0.75x + 0.140625 + x2 = 1.5 + 0.140625

Reorder the terms:
0.140625 + 0.75x + x2 = 1.5 + 0.140625

Combine like terms: 1.5 + 0.140625 = 1.640625
0.140625 + 0.75x + x2 = 1.640625

Factor a perfect square on the left side:
(x + 0.375)(x + 0.375) = 1.640625

Calculate the square root of the right side: 1.280868846

Break this problem into two subproblems by setting 
(x + 0.375) equal to 1.280868846 and -1.280868846.

Subproblem 1
x + 0.375 = 1.280868846

Simplifying
x + 0.375 = 1.280868846

Reorder the terms:
0.375 + x = 1.280868846

Solving
0.375 + x = 1.280868846

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = 1.280868846 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = 1.280868846 + -0.375
x = 1.280868846 + -0.375

Combine like terms: 1.280868846 + -0.375 = 0.905868846
x = 0.905868846

Simplifying
x = 0.905868846

Subproblem 2
x + 0.375 = -1.280868846

Simplifying
x + 0.375 = -1.280868846

Reorder the terms:
0.375 + x = -1.280868846

Solving
0.375 + x = -1.280868846

Solving for variable 'x'.

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

Add '-0.375' to each side of the equation.
0.375 + -0.375 + x = -1.280868846 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + x = -1.280868846 + -0.375
x = -1.280868846 + -0.375

Combine like terms: -1.280868846 + -0.375 = -1.655868846
x = -1.655868846

Simplifying
x = -1.655868846

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.905868846, -1.655868846}
Solution
x = {0.905868846, -1.655868846}