24x^2+12x+21=0

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Solution for 24x^2+12x+21=0 equation: 


Simplifying
24x2 + 12x + 21 = 0

Reorder the terms:
21 + 12x + 24x2 = 0

Solving
21 + 12x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 4x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 4x + 8x2)' equal to zero and attempt to solve:

Simplifying
7 + 4x + 8x2 = 0

Solving
7 + 4x + 8x2 = 0

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

Divide each side by '8'.
0.875 + 0.5x + x2 = 0

Move the constant term to the right:

Add '-0.875' to each side of the equation.
0.875 + 0.5x + -0.875 + x2 = 0 + -0.875

Reorder the terms:
0.875 + -0.875 + 0.5x + x2 = 0 + -0.875

Combine like terms: 0.875 + -0.875 = 0.000
0.000 + 0.5x + x2 = 0 + -0.875
0.5x + x2 = 0 + -0.875

Combine like terms: 0 + -0.875 = -0.875
0.5x + x2 = -0.875

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = -0.875 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = -0.875 + 0.0625

Combine like terms: -0.875 + 0.0625 = -0.8125
0.0625 + 0.5x + x2 = -0.8125

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = -0.8125

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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