9a(2a^2-5a-6)-5a(a-5)=

Solution for 9a(2a^2-5a-6)-5a(a-5)= equation:

Simplifying
9a(2a2 + -5a + -6) + -5a(a + -5) = 0

Reorder the terms:
9a(-6 + -5a + 2a2) + -5a(a + -5) = 0
(-6 * 9a + -5a * 9a + 2a2 * 9a) + -5a(a + -5) = 0
(-54a + -45a2 + 18a3) + -5a(a + -5) = 0

Reorder the terms:
-54a + -45a2 + 18a3 + -5a(-5 + a) = 0
-54a + -45a2 + 18a3 + (-5 * -5a + a * -5a) = 0
-54a + -45a2 + 18a3 + (25a + -5a2) = 0

Reorder the terms:
-54a + 25a + -45a2 + -5a2 + 18a3 = 0

Combine like terms: -54a + 25a = -29a
-29a + -45a2 + -5a2 + 18a3 = 0

Combine like terms: -45a2 + -5a2 = -50a2
-29a + -50a2 + 18a3 = 0

Solving
-29a + -50a2 + 18a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-29 + -50a + 18a2) = 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 '(-29 + -50a + 18a2)' equal to zero and attempt to solve:

Simplifying
-29 + -50a + 18a2 = 0

Solving
-29 + -50a + 18a2 = 0

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

Divide each side by '18'.
-1.611111111 + -2.777777778a + a2 = 0

Move the constant term to the right:

Add '1.611111111' to each side of the equation.
-1.611111111 + -2.777777778a + 1.611111111 + a2 = 0 + 1.611111111

Reorder the terms:
-1.611111111 + 1.611111111 + -2.777777778a + a2 = 0 + 1.611111111

Combine like terms: -1.611111111 + 1.611111111 = 0.000000000
0.000000000 + -2.777777778a + a2 = 0 + 1.611111111
-2.777777778a + a2 = 0 + 1.611111111

Combine like terms: 0 + 1.611111111 = 1.611111111
-2.777777778a + a2 = 1.611111111

The a term is -2.777777778a.  Take half its coefficient (-1.388888889).
Square it (1.929012346) and add it to both sides.

Add '1.929012346' to each side of the equation.
-2.777777778a + 1.929012346 + a2 = 1.611111111 + 1.929012346

Reorder the terms:
1.929012346 + -2.777777778a + a2 = 1.611111111 + 1.929012346

Combine like terms: 1.611111111 + 1.929012346 = 3.540123457
1.929012346 + -2.777777778a + a2 = 3.540123457

Factor a perfect square on the left side:
(a + -1.388888889)(a + -1.388888889) = 3.540123457

Calculate the square root of the right side: 1.88152158

Break this problem into two subproblems by setting 
(a + -1.388888889) equal to 1.88152158 and -1.88152158.

Subproblem 1
a + -1.388888889 = 1.88152158

Simplifying
a + -1.388888889 = 1.88152158

Reorder the terms:
-1.388888889 + a = 1.88152158

Solving
-1.388888889 + a = 1.88152158

Solving for variable 'a'.

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

Add '1.388888889' to each side of the equation.
-1.388888889 + 1.388888889 + a = 1.88152158 + 1.388888889

Combine like terms: -1.388888889 + 1.388888889 = 0.000000000
0.000000000 + a = 1.88152158 + 1.388888889
a = 1.88152158 + 1.388888889

Combine like terms: 1.88152158 + 1.388888889 = 3.270410469
a = 3.270410469

Simplifying
a = 3.270410469

Subproblem 2
a + -1.388888889 = -1.88152158

Simplifying
a + -1.388888889 = -1.88152158

Reorder the terms:
-1.388888889 + a = -1.88152158

Solving
-1.388888889 + a = -1.88152158

Solving for variable 'a'.

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

Add '1.388888889' to each side of the equation.
-1.388888889 + 1.388888889 + a = -1.88152158 + 1.388888889

Combine like terms: -1.388888889 + 1.388888889 = 0.000000000
0.000000000 + a = -1.88152158 + 1.388888889
a = -1.88152158 + 1.388888889

Combine like terms: -1.88152158 + 1.388888889 = -0.492632691
a = -0.492632691

Simplifying
a = -0.492632691

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {3.270410469, -0.492632691}
Solution
a = {0, 3.270410469, -0.492632691}