12x^2+32x+80=0

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Solution for 12x^2+32x+80=0 equation: 


Simplifying
12x2 + 32x + 80 = 0

Reorder the terms:
80 + 32x + 12x2 = 0

Solving
80 + 32x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(20 + 8x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(20 + 8x + 3x2)' equal to zero and attempt to solve:

Simplifying
20 + 8x + 3x2 = 0

Solving
20 + 8x + 3x2 = 0

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

Divide each side by '3'.
6.666666667 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-6.666666667' to each side of the equation.
6.666666667 + 2.666666667x + -6.666666667 + x2 = 0 + -6.666666667

Reorder the terms:
6.666666667 + -6.666666667 + 2.666666667x + x2 = 0 + -6.666666667

Combine like terms: 6.666666667 + -6.666666667 = 0.000000000
0.000000000 + 2.666666667x + x2 = 0 + -6.666666667
2.666666667x + x2 = 0 + -6.666666667

Combine like terms: 0 + -6.666666667 = -6.666666667
2.666666667x + x2 = -6.666666667

The x term is 2.666666667x.  Take half its coefficient (1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
2.666666667x + 1.777777780 + x2 = -6.666666667 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -6.666666667 + 1.777777780

Combine like terms: -6.666666667 + 1.777777780 = -4.888888887
1.777777780 + 2.666666667x + x2 = -4.888888887

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -4.888888887

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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