0=6+32x+16x^2

Solution for 0=6+32x+16x^2 equation:

Simplifying
0 = 6 + 32x + 16x2

Solving
0 = 6 + 32x + 16x2

Solving for variable 'x'.

Combine like terms: 0 + -6 = -6
-6 + -32x + -16x2 = 6 + 32x + 16x2 + -6 + -32x + -16x2

Reorder the terms:
-6 + -32x + -16x2 = 6 + -6 + 32x + -32x + 16x2 + -16x2

Combine like terms: 6 + -6 = 0
-6 + -32x + -16x2 = 0 + 32x + -32x + 16x2 + -16x2
-6 + -32x + -16x2 = 32x + -32x + 16x2 + -16x2

Combine like terms: 32x + -32x = 0
-6 + -32x + -16x2 = 0 + 16x2 + -16x2
-6 + -32x + -16x2 = 16x2 + -16x2

Combine like terms: 16x2 + -16x2 = 0
-6 + -32x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(3 + 16x + 8x2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(3 + 16x + 8x2)' equal to zero and attempt to solve:

Simplifying
3 + 16x + 8x2 = 0

Solving
3 + 16x + 8x2 = 0

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

Divide each side by '8'.
0.375 + 2x + x2 = 0

Move the constant term to the right:

Add '-0.375' to each side of the equation.
0.375 + 2x + -0.375 + x2 = 0 + -0.375

Reorder the terms:
0.375 + -0.375 + 2x + x2 = 0 + -0.375

Combine like terms: 0.375 + -0.375 = 0.000
0.000 + 2x + x2 = 0 + -0.375
2x + x2 = 0 + -0.375

Combine like terms: 0 + -0.375 = -0.375
2x + x2 = -0.375

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -0.375 + 1

Reorder the terms:
1 + 2x + x2 = -0.375 + 1

Combine like terms: -0.375 + 1 = 0.625
1 + 2x + x2 = 0.625

Factor a perfect square on the left side:
(x + 1)(x + 1) = 0.625

Calculate the square root of the right side: 0.790569415

Break this problem into two subproblems by setting 
(x + 1) equal to 0.790569415 and -0.790569415.

Subproblem 1
x + 1 = 0.790569415

Simplifying
x + 1 = 0.790569415

Reorder the terms:
1 + x = 0.790569415

Solving
1 + x = 0.790569415

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 0.790569415 + -1

Combine like terms: 1 + -1 = 0
0 + x = 0.790569415 + -1
x = 0.790569415 + -1

Combine like terms: 0.790569415 + -1 = -0.209430585
x = -0.209430585

Simplifying
x = -0.209430585

Subproblem 2
x + 1 = -0.790569415

Simplifying
x + 1 = -0.790569415

Reorder the terms:
1 + x = -0.790569415

Solving
1 + x = -0.790569415

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -0.790569415 + -1

Combine like terms: 1 + -1 = 0
0 + x = -0.790569415 + -1
x = -0.790569415 + -1

Combine like terms: -0.790569415 + -1 = -1.790569415
x = -1.790569415

Simplifying
x = -1.790569415

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.209430585, -1.790569415}
Solution
x = {-0.209430585, -1.790569415}