18a^3-24a^2+35a^3-30a^2+25a-3a^2-18a=

Solution for 18a^3-24a^2+35a^3-30a^2+25a-3a^2-18a= equation:

Simplifying
18a3 + -24a2 + 35a3 + -30a2 + 25a + -3a2 + -18a = 0

Reorder the terms:
25a + -18a + -24a2 + -30a2 + -3a2 + 18a3 + 35a3 = 0

Combine like terms: 25a + -18a = 7a
7a + -24a2 + -30a2 + -3a2 + 18a3 + 35a3 = 0

Combine like terms: -24a2 + -30a2 = -54a2
7a + -54a2 + -3a2 + 18a3 + 35a3 = 0

Combine like terms: -54a2 + -3a2 = -57a2
7a + -57a2 + 18a3 + 35a3 = 0

Combine like terms: 18a3 + 35a3 = 53a3
7a + -57a2 + 53a3 = 0

Solving
7a + -57a2 + 53a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(7 + -57a + 53a2) = 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 '(7 + -57a + 53a2)' equal to zero and attempt to solve:

Simplifying
7 + -57a + 53a2 = 0

Solving
7 + -57a + 53a2 = 0

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

Divide each side by '53'.
0.1320754717 + -1.075471698a + a2 = 0

Move the constant term to the right:

Add '-0.1320754717' to each side of the equation.
0.1320754717 + -1.075471698a + -0.1320754717 + a2 = 0 + -0.1320754717

Reorder the terms:
0.1320754717 + -0.1320754717 + -1.075471698a + a2 = 0 + -0.1320754717

Combine like terms: 0.1320754717 + -0.1320754717 = 0.0000000000
0.0000000000 + -1.075471698a + a2 = 0 + -0.1320754717
-1.075471698a + a2 = 0 + -0.1320754717

Combine like terms: 0 + -0.1320754717 = -0.1320754717
-1.075471698a + a2 = -0.1320754717

The a term is -1.075471698a.  Take half its coefficient (-0.537735849).
Square it (0.2891598433) and add it to both sides.

Add '0.2891598433' to each side of the equation.
-1.075471698a + 0.2891598433 + a2 = -0.1320754717 + 0.2891598433

Reorder the terms:
0.2891598433 + -1.075471698a + a2 = -0.1320754717 + 0.2891598433

Combine like terms: -0.1320754717 + 0.2891598433 = 0.1570843716
0.2891598433 + -1.075471698a + a2 = 0.1570843716

Factor a perfect square on the left side:
(a + -0.537735849)(a + -0.537735849) = 0.1570843716

Calculate the square root of the right side: 0.396338708

Break this problem into two subproblems by setting 
(a + -0.537735849) equal to 0.396338708 and -0.396338708.

Subproblem 1
a + -0.537735849 = 0.396338708

Simplifying
a + -0.537735849 = 0.396338708

Reorder the terms:
-0.537735849 + a = 0.396338708

Solving
-0.537735849 + a = 0.396338708

Solving for variable 'a'.

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

Add '0.537735849' to each side of the equation.
-0.537735849 + 0.537735849 + a = 0.396338708 + 0.537735849

Combine like terms: -0.537735849 + 0.537735849 = 0.000000000
0.000000000 + a = 0.396338708 + 0.537735849
a = 0.396338708 + 0.537735849

Combine like terms: 0.396338708 + 0.537735849 = 0.934074557
a = 0.934074557

Simplifying
a = 0.934074557

Subproblem 2
a + -0.537735849 = -0.396338708

Simplifying
a + -0.537735849 = -0.396338708

Reorder the terms:
-0.537735849 + a = -0.396338708

Solving
-0.537735849 + a = -0.396338708

Solving for variable 'a'.

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

Add '0.537735849' to each side of the equation.
-0.537735849 + 0.537735849 + a = -0.396338708 + 0.537735849

Combine like terms: -0.537735849 + 0.537735849 = 0.000000000
0.000000000 + a = -0.396338708 + 0.537735849
a = -0.396338708 + 0.537735849

Combine like terms: -0.396338708 + 0.537735849 = 0.141397141
a = 0.141397141

Simplifying
a = 0.141397141

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.934074557, 0.141397141}
Solution
a = {0, 0.934074557, 0.141397141}