6x^2+20x+32=0

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Solution for 6x^2+20x+32=0 equation: 


Simplifying
6x2 + 20x + 32 = 0

Reorder the terms:
32 + 20x + 6x2 = 0

Solving
32 + 20x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(16 + 10x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(16 + 10x + 3x2)' equal to zero and attempt to solve:

Simplifying
16 + 10x + 3x2 = 0

Solving
16 + 10x + 3x2 = 0

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

Divide each side by '3'.
5.333333333 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '-5.333333333' to each side of the equation.
5.333333333 + 3.333333333x + -5.333333333 + x2 = 0 + -5.333333333

Reorder the terms:
5.333333333 + -5.333333333 + 3.333333333x + x2 = 0 + -5.333333333

Combine like terms: 5.333333333 + -5.333333333 = 0.000000000
0.000000000 + 3.333333333x + x2 = 0 + -5.333333333
3.333333333x + x2 = 0 + -5.333333333

Combine like terms: 0 + -5.333333333 = -5.333333333
3.333333333x + x2 = -5.333333333

The x term is 3.333333333x.  Take half its coefficient (1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
3.333333333x + 2.777777779 + x2 = -5.333333333 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = -5.333333333 + 2.777777779

Combine like terms: -5.333333333 + 2.777777779 = -2.555555554
2.777777779 + 3.333333333x + x2 = -2.555555554

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = -2.555555554

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.

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