3(a^2+2a-6)+2[3(2a^2-3a+2)-2(a^2-4a-5)]=0

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Solution for 3(a^2+2a-6)+2[3(2a^2-3a+2)-2(a^2-4a-5)]=0 equation: 


Simplifying
3(a2 + 2a + -6) + 2[3(2a2 + -3a + 2) + -2(a2 + -4a + -5)] = 0

Reorder the terms:
3(-6 + 2a + a2) + 2[3(2a2 + -3a + 2) + -2(a2 + -4a + -5)] = 0
(-6 * 3 + 2a * 3 + a2 * 3) + 2[3(2a2 + -3a + 2) + -2(a2 + -4a + -5)] = 0
(-18 + 6a + 3a2) + 2[3(2a2 + -3a + 2) + -2(a2 + -4a + -5)] = 0

Reorder the terms:
-18 + 6a + 3a2 + 2[3(2 + -3a + 2a2) + -2(a2 + -4a + -5)] = 0
-18 + 6a + 3a2 + 2[(2 * 3 + -3a * 3 + 2a2 * 3) + -2(a2 + -4a + -5)] = 0
-18 + 6a + 3a2 + 2[(6 + -9a + 6a2) + -2(a2 + -4a + -5)] = 0

Reorder the terms:
-18 + 6a + 3a2 + 2[6 + -9a + 6a2 + -2(-5 + -4a + a2)] = 0
-18 + 6a + 3a2 + 2[6 + -9a + 6a2 + (-5 * -2 + -4a * -2 + a2 * -2)] = 0
-18 + 6a + 3a2 + 2[6 + -9a + 6a2 + (10 + 8a + -2a2)] = 0

Reorder the terms:
-18 + 6a + 3a2 + 2[6 + 10 + -9a + 8a + 6a2 + -2a2] = 0

Combine like terms: 6 + 10 = 16
-18 + 6a + 3a2 + 2[16 + -9a + 8a + 6a2 + -2a2] = 0

Combine like terms: -9a + 8a = -1a
-18 + 6a + 3a2 + 2[16 + -1a + 6a2 + -2a2] = 0

Combine like terms: 6a2 + -2a2 = 4a2
-18 + 6a + 3a2 + 2[16 + -1a + 4a2] = 0
-18 + 6a + 3a2 + [16 * 2 + -1a * 2 + 4a2 * 2] = 0
-18 + 6a + 3a2 + [32 + -2a + 8a2] = 0

Reorder the terms:
-18 + 32 + 6a + -2a + 3a2 + 8a2 = 0

Combine like terms: -18 + 32 = 14
14 + 6a + -2a + 3a2 + 8a2 = 0

Combine like terms: 6a + -2a = 4a
14 + 4a + 3a2 + 8a2 = 0

Combine like terms: 3a2 + 8a2 = 11a2
14 + 4a + 11a2 = 0

Solving
14 + 4a + 11a2 = 0

Solving for variable 'a'.

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

Divide each side by '11'.
1.272727273 + 0.3636363636a + a2 = 0

Move the constant term to the right:

Add '-1.272727273' to each side of the equation.
1.272727273 + 0.3636363636a + -1.272727273 + a2 = 0 + -1.272727273

Reorder the terms:
1.272727273 + -1.272727273 + 0.3636363636a + a2 = 0 + -1.272727273

Combine like terms: 1.272727273 + -1.272727273 = 0.000000000
0.000000000 + 0.3636363636a + a2 = 0 + -1.272727273
0.3636363636a + a2 = 0 + -1.272727273

Combine like terms: 0 + -1.272727273 = -1.272727273
0.3636363636a + a2 = -1.272727273

The a term is 0.3636363636a.  Take half its coefficient (0.1818181818).
Square it (0.03305785123) and add it to both sides.

Add '0.03305785123' to each side of the equation.
0.3636363636a + 0.03305785123 + a2 = -1.272727273 + 0.03305785123

Reorder the terms:
0.03305785123 + 0.3636363636a + a2 = -1.272727273 + 0.03305785123

Combine like terms: -1.272727273 + 0.03305785123 = -1.23966942177
0.03305785123 + 0.3636363636a + a2 = -1.23966942177

Factor a perfect square on the left side:
(a + 0.1818181818)(a + 0.1818181818) = -1.23966942177

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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