(2a^3+3a^2+7a)+(a^3+a^2-2a)=

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Solution for (2a^3+3a^2+7a)+(a^3+a^2-2a)= equation: 


Simplifying
(2a3 + 3a2 + 7a) + (a3 + a2 + -2a) = 0

Reorder the terms:
(7a + 3a2 + 2a3) + (a3 + a2 + -2a) = 0

Remove parenthesis around (7a + 3a2 + 2a3)
7a + 3a2 + 2a3 + (a3 + a2 + -2a) = 0

Reorder the terms:
7a + 3a2 + 2a3 + (-2a + a2 + a3) = 0

Remove parenthesis around (-2a + a2 + a3)
7a + 3a2 + 2a3 + -2a + a2 + a3 = 0

Reorder the terms:
7a + -2a + 3a2 + a2 + 2a3 + a3 = 0

Combine like terms: 7a + -2a = 5a
5a + 3a2 + a2 + 2a3 + a3 = 0

Combine like terms: 3a2 + a2 = 4a2
5a + 4a2 + 2a3 + a3 = 0

Combine like terms: 2a3 + a3 = 3a3
5a + 4a2 + 3a3 = 0

Solving
5a + 4a2 + 3a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(5 + 4a + 3a2) = 0


Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

Move all terms containing a to the left, all other terms to the right.

Simplifying
a = 0

Subproblem 2
Set the factor '(5 + 4a + 3a2)' equal to zero and attempt to solve:

Simplifying
5 + 4a + 3a2 = 0

Solving
5 + 4a + 3a2 = 0

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

Divide each side by '3'.
1.666666667 + 1.333333333a + a2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + 1.333333333a + -1.666666667 + a2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + 1.333333333a + a2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + 1.333333333a + a2 = 0 + -1.666666667
1.333333333a + a2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
1.333333333a + a2 = -1.666666667

The a term is 1.333333333a.  Take half its coefficient (0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
1.333333333a + 0.4444444442 + a2 = -1.666666667 + 0.4444444442

Reorder the terms:
0.4444444442 + 1.333333333a + a2 = -1.666666667 + 0.4444444442

Combine like terms: -1.666666667 + 0.4444444442 = -1.2222222228
0.4444444442 + 1.333333333a + a2 = -1.2222222228

Factor a perfect square on the left side:
(a + 0.6666666665)(a + 0.6666666665) = -1.2222222228

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.
Solution
a = {0}

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