9a(3a^2-5a-5)-5a(a-2)=

Solution for 9a(3a^2-5a-5)-5a(a-2)= equation:

Simplifying
9a(3a2 + -5a + -5) + -5a(a + -2) = 0

Reorder the terms:
9a(-5 + -5a + 3a2) + -5a(a + -2) = 0
(-5 * 9a + -5a * 9a + 3a2 * 9a) + -5a(a + -2) = 0
(-45a + -45a2 + 27a3) + -5a(a + -2) = 0

Reorder the terms:
-45a + -45a2 + 27a3 + -5a(-2 + a) = 0
-45a + -45a2 + 27a3 + (-2 * -5a + a * -5a) = 0
-45a + -45a2 + 27a3 + (10a + -5a2) = 0

Reorder the terms:
-45a + 10a + -45a2 + -5a2 + 27a3 = 0

Combine like terms: -45a + 10a = -35a
-35a + -45a2 + -5a2 + 27a3 = 0

Combine like terms: -45a2 + -5a2 = -50a2
-35a + -50a2 + 27a3 = 0

Solving
-35a + -50a2 + 27a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-35 + -50a + 27a2) = 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 '(-35 + -50a + 27a2)' equal to zero and attempt to solve:

Simplifying
-35 + -50a + 27a2 = 0

Solving
-35 + -50a + 27a2 = 0

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

Divide each side by '27'.
-1.296296296 + -1.851851852a + a2 = 0

Move the constant term to the right:

Add '1.296296296' to each side of the equation.
-1.296296296 + -1.851851852a + 1.296296296 + a2 = 0 + 1.296296296

Reorder the terms:
-1.296296296 + 1.296296296 + -1.851851852a + a2 = 0 + 1.296296296

Combine like terms: -1.296296296 + 1.296296296 = 0.000000000
0.000000000 + -1.851851852a + a2 = 0 + 1.296296296
-1.851851852a + a2 = 0 + 1.296296296

Combine like terms: 0 + 1.296296296 = 1.296296296
-1.851851852a + a2 = 1.296296296

The a term is -1.851851852a.  Take half its coefficient (-0.925925926).
Square it (0.8573388204) and add it to both sides.

Add '0.8573388204' to each side of the equation.
-1.851851852a + 0.8573388204 + a2 = 1.296296296 + 0.8573388204

Reorder the terms:
0.8573388204 + -1.851851852a + a2 = 1.296296296 + 0.8573388204

Combine like terms: 1.296296296 + 0.8573388204 = 2.1536351164
0.8573388204 + -1.851851852a + a2 = 2.1536351164

Factor a perfect square on the left side:
(a + -0.925925926)(a + -0.925925926) = 2.1536351164

Calculate the square root of the right side: 1.467526871

Break this problem into two subproblems by setting 
(a + -0.925925926) equal to 1.467526871 and -1.467526871.

Subproblem 1
a + -0.925925926 = 1.467526871

Simplifying
a + -0.925925926 = 1.467526871

Reorder the terms:
-0.925925926 + a = 1.467526871

Solving
-0.925925926 + a = 1.467526871

Solving for variable 'a'.

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

Add '0.925925926' to each side of the equation.
-0.925925926 + 0.925925926 + a = 1.467526871 + 0.925925926

Combine like terms: -0.925925926 + 0.925925926 = 0.000000000
0.000000000 + a = 1.467526871 + 0.925925926
a = 1.467526871 + 0.925925926

Combine like terms: 1.467526871 + 0.925925926 = 2.393452797
a = 2.393452797

Simplifying
a = 2.393452797

Subproblem 2
a + -0.925925926 = -1.467526871

Simplifying
a + -0.925925926 = -1.467526871

Reorder the terms:
-0.925925926 + a = -1.467526871

Solving
-0.925925926 + a = -1.467526871

Solving for variable 'a'.

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

Add '0.925925926' to each side of the equation.
-0.925925926 + 0.925925926 + a = -1.467526871 + 0.925925926

Combine like terms: -0.925925926 + 0.925925926 = 0.000000000
0.000000000 + a = -1.467526871 + 0.925925926
a = -1.467526871 + 0.925925926

Combine like terms: -1.467526871 + 0.925925926 = -0.541600945
a = -0.541600945

Simplifying
a = -0.541600945

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {2.393452797, -0.541600945}
Solution
a = {0, 2.393452797, -0.541600945}