4(3x^2+14x+24)=0

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Solution for 4(3x^2+14x+24)=0 equation: 


Simplifying
4(3x2 + 14x + 24) = 0

Reorder the terms:
4(24 + 14x + 3x2) = 0
(24 * 4 + 14x * 4 + 3x2 * 4) = 0
(96 + 56x + 12x2) = 0

Solving
96 + 56x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(24 + 14x + 3x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(24 + 14x + 3x2)' equal to zero and attempt to solve:

Simplifying
24 + 14x + 3x2 = 0

Solving
24 + 14x + 3x2 = 0

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

Divide each side by '3'.
8 + 4.666666667x + x2 = 0

Move the constant term to the right:

Add '-8' to each side of the equation.
8 + 4.666666667x + -8 + x2 = 0 + -8

Reorder the terms:
8 + -8 + 4.666666667x + x2 = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 4.666666667x + x2 = 0 + -8
4.666666667x + x2 = 0 + -8

Combine like terms: 0 + -8 = -8
4.666666667x + x2 = -8

The x term is 4.666666667x.  Take half its coefficient (2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
4.666666667x + 5.444444448 + x2 = -8 + 5.444444448

Reorder the terms:
5.444444448 + 4.666666667x + x2 = -8 + 5.444444448

Combine like terms: -8 + 5.444444448 = -2.555555552
5.444444448 + 4.666666667x + x2 = -2.555555552

Factor a perfect square on the left side:
(x + 2.333333334)(x + 2.333333334) = -2.555555552

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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