6x^2+64x+192=0

Solution for 6x^2+64x+192=0 equation:

Simplifying
6x2 + 64x + 192 = 0

Reorder the terms:
192 + 64x + 6x2 = 0

Solving
192 + 64x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(96 + 32x + 3x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(96 + 32x + 3x2)' equal to zero and attempt to solve:

Simplifying
96 + 32x + 3x2 = 0

Solving
96 + 32x + 3x2 = 0

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

Divide each side by '3'.
32 + 10.66666667x + x2 = 0

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + 10.66666667x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + 10.66666667x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + 10.66666667x + x2 = 0 + -32
10.66666667x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
10.66666667x + x2 = -32

The x term is 10.66666667x.  Take half its coefficient (5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
10.66666667x + 28.44444446 + x2 = -32 + 28.44444446

Reorder the terms:
28.44444446 + 10.66666667x + x2 = -32 + 28.44444446

Combine like terms: -32 + 28.44444446 = -3.55555554
28.44444446 + 10.66666667x + x2 = -3.55555554

Factor a perfect square on the left side:
(x + 5.333333335)(x + 5.333333335) = -3.55555554

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.