6x^2+16x+60=0

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Solution for 6x^2+16x+60=0 equation: 


Simplifying
6x2 + 16x + 60 = 0

Reorder the terms:
60 + 16x + 6x2 = 0

Solving
60 + 16x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(30 + 8x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(30 + 8x + 3x2)' equal to zero and attempt to solve:

Simplifying
30 + 8x + 3x2 = 0

Solving
30 + 8x + 3x2 = 0

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

Divide each side by '3'.
10 + 2.666666667x + x2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 2.666666667x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 2.666666667x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 2.666666667x + x2 = 0 + -10
2.666666667x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
2.666666667x + x2 = -10

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 = -10 + 1.777777780

Reorder the terms:
1.777777780 + 2.666666667x + x2 = -10 + 1.777777780

Combine like terms: -10 + 1.777777780 = -8.22222222
1.777777780 + 2.666666667x + x2 = -8.22222222

Factor a perfect square on the left side:
(x + 1.333333334)(x + 1.333333334) = -8.22222222

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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