3a(a+2)*5a+2a*(a+3)(a-1)=

Solution for 3a(a+2)*5a+2a*(a+3)(a-1)= equation:

Simplifying
3a(a + 2) * 5a + 2a(a + 3)(a + -1) = 0

Reorder the terms:
3a(2 + a) * 5a + 2a(a + 3)(a + -1) = 0

Reorder the terms for easier multiplication:
3 * 5a * a(2 + a) + 2a(a + 3)(a + -1) = 0

Multiply 3 * 5
15a * a(2 + a) + 2a(a + 3)(a + -1) = 0

Multiply a * a
15a2(2 + a) + 2a(a + 3)(a + -1) = 0
(2 * 15a2 + a * 15a2) + 2a(a + 3)(a + -1) = 0
(30a2 + 15a3) + 2a(a + 3)(a + -1) = 0

Reorder the terms:
30a2 + 15a3 + 2a(3 + a)(a + -1) = 0

Reorder the terms:
30a2 + 15a3 + 2a(3 + a)(-1 + a) = 0

Multiply (3 + a) * (-1 + a)
30a2 + 15a3 + 2a(3(-1 + a) + a(-1 + a)) = 0
30a2 + 15a3 + 2a((-1 * 3 + a * 3) + a(-1 + a)) = 0
30a2 + 15a3 + 2a((-3 + 3a) + a(-1 + a)) = 0
30a2 + 15a3 + 2a(-3 + 3a + (-1 * a + a * a)) = 0
30a2 + 15a3 + 2a(-3 + 3a + (-1a + a2)) = 0

Combine like terms: 3a + -1a = 2a
30a2 + 15a3 + 2a(-3 + 2a + a2) = 0
30a2 + 15a3 + (-3 * 2a + 2a * 2a + a2 * 2a) = 0
30a2 + 15a3 + (-6a + 4a2 + 2a3) = 0

Reorder the terms:
-6a + 30a2 + 4a2 + 15a3 + 2a3 = 0

Combine like terms: 30a2 + 4a2 = 34a2
-6a + 34a2 + 15a3 + 2a3 = 0

Combine like terms: 15a3 + 2a3 = 17a3
-6a + 34a2 + 17a3 = 0

Solving
-6a + 34a2 + 17a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(-6 + 34a + 17a2) = 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 '(-6 + 34a + 17a2)' equal to zero and attempt to solve:

Simplifying
-6 + 34a + 17a2 = 0

Solving
-6 + 34a + 17a2 = 0

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

Divide each side by '17'.
-0.3529411765 + 2a + a2 = 0

Move the constant term to the right:

Add '0.3529411765' to each side of the equation.
-0.3529411765 + 2a + 0.3529411765 + a2 = 0 + 0.3529411765

Reorder the terms:
-0.3529411765 + 0.3529411765 + 2a + a2 = 0 + 0.3529411765

Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000
0.0000000000 + 2a + a2 = 0 + 0.3529411765
2a + a2 = 0 + 0.3529411765

Combine like terms: 0 + 0.3529411765 = 0.3529411765
2a + a2 = 0.3529411765

The a term is 2a.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2a + 1 + a2 = 0.3529411765 + 1

Reorder the terms:
1 + 2a + a2 = 0.3529411765 + 1

Combine like terms: 0.3529411765 + 1 = 1.3529411765
1 + 2a + a2 = 1.3529411765

Factor a perfect square on the left side:
(a + 1)(a + 1) = 1.3529411765

Calculate the square root of the right side: 1.163159996

Break this problem into two subproblems by setting 
(a + 1) equal to 1.163159996 and -1.163159996.

Subproblem 1
a + 1 = 1.163159996

Simplifying
a + 1 = 1.163159996

Reorder the terms:
1 + a = 1.163159996

Solving
1 + a = 1.163159996

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = 1.163159996 + -1

Combine like terms: 1 + -1 = 0
0 + a = 1.163159996 + -1
a = 1.163159996 + -1

Combine like terms: 1.163159996 + -1 = 0.163159996
a = 0.163159996

Simplifying
a = 0.163159996

Subproblem 2
a + 1 = -1.163159996

Simplifying
a + 1 = -1.163159996

Reorder the terms:
1 + a = -1.163159996

Solving
1 + a = -1.163159996

Solving for variable 'a'.

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

Add '-1' to each side of the equation.
1 + -1 + a = -1.163159996 + -1

Combine like terms: 1 + -1 = 0
0 + a = -1.163159996 + -1
a = -1.163159996 + -1

Combine like terms: -1.163159996 + -1 = -2.163159996
a = -2.163159996

Simplifying
a = -2.163159996

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.163159996, -2.163159996}
Solution
a = {0, 0.163159996, -2.163159996}