16x^2-8x-6=0

Solution for 16x^2-8x-6=0 equation:

Simplifying
16x2 + -8x + -6 = 0

Reorder the terms:
-6 + -8x + 16x2 = 0

Solving
-6 + -8x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -4x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -4x + 8x2)' equal to zero and attempt to solve:

Simplifying
-3 + -4x + 8x2 = 0

Solving
-3 + -4x + 8x2 = 0

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

Divide each side by '8'.
-0.375 + -0.5x + x2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -0.5x + 0.375 + x2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -0.5x + x2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -0.5x + x2 = 0 + 0.375
-0.5x + x2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-0.5x + x2 = 0.375

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 0.375 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 0.375 + 0.0625

Combine like terms: 0.375 + 0.0625 = 0.4375
0.0625 + -0.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + -0.25) equal to 0.661437828 and -0.661437828.

Subproblem 1
x + -0.25 = 0.661437828

Simplifying
x + -0.25 = 0.661437828

Reorder the terms:
-0.25 + x = 0.661437828

Solving
-0.25 + x = 0.661437828

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = 0.661437828 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = 0.661437828 + 0.25
x = 0.661437828 + 0.25

Combine like terms: 0.661437828 + 0.25 = 0.911437828
x = 0.911437828

Simplifying
x = 0.911437828

Subproblem 2
x + -0.25 = -0.661437828

Simplifying
x + -0.25 = -0.661437828

Reorder the terms:
-0.25 + x = -0.661437828

Solving
-0.25 + x = -0.661437828

Solving for variable 'x'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + x = -0.661437828 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + x = -0.661437828 + 0.25
x = -0.661437828 + 0.25

Combine like terms: -0.661437828 + 0.25 = -0.411437828
x = -0.411437828

Simplifying
x = -0.411437828

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.911437828, -0.411437828}
Solution
x = {0.911437828, -0.411437828}