6a+24=-9a^2

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Solution for 6a+24=-9a^2 equation: 


Simplifying
6a + 24 = -9a2

Reorder the terms:
24 + 6a = -9a2

Solving
24 + 6a = -9a2

Solving for variable 'a'.

Combine like terms: -9a2 + 9a2 = 0
24 + 6a + 9a2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(8 + 2a + 3a2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(8 + 2a + 3a2)' equal to zero and attempt to solve:

Simplifying
8 + 2a + 3a2 = 0

Solving
8 + 2a + 3a2 = 0

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

Divide each side by '3'.
2.666666667 + 0.6666666667a + a2 = 0

Move the constant term to the right:

Add '-2.666666667' to each side of the equation.
2.666666667 + 0.6666666667a + -2.666666667 + a2 = 0 + -2.666666667

Reorder the terms:
2.666666667 + -2.666666667 + 0.6666666667a + a2 = 0 + -2.666666667

Combine like terms: 2.666666667 + -2.666666667 = 0.000000000
0.000000000 + 0.6666666667a + a2 = 0 + -2.666666667
0.6666666667a + a2 = 0 + -2.666666667

Combine like terms: 0 + -2.666666667 = -2.666666667
0.6666666667a + a2 = -2.666666667

The a term is 0.6666666667a.  Take half its coefficient (0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
0.6666666667a + 0.1111111112 + a2 = -2.666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + 0.6666666667a + a2 = -2.666666667 + 0.1111111112

Combine like terms: -2.666666667 + 0.1111111112 = -2.5555555558
0.1111111112 + 0.6666666667a + a2 = -2.5555555558

Factor a perfect square on the left side:
(a + 0.3333333334)(a + 0.3333333334) = -2.5555555558

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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