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 = 26a2
6a + 26a2 + 15a3 + -2a3 = 0

Combine like terms: 15a3 + -2a3 = 13a3
6a + 26a2 + 13a3 = 0

Solving
6a + 26a2 + 13a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), 'a'.
a(6 + 26a + 13a2) = 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 + 26a + 13a2)' equal to zero and attempt to solve:

Simplifying
6 + 26a + 13a2 = 0

Solving
6 + 26a + 13a2 = 0

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

Divide each side by '13'.
0.4615384615 + 2a + a2 = 0

Move the constant term to the right:

Add '-0.4615384615' to each side of the equation.
0.4615384615 + 2a + -0.4615384615 + a2 = 0 + -0.4615384615

Reorder the terms:
0.4615384615 + -0.4615384615 + 2a + a2 = 0 + -0.4615384615

Combine like terms: 0.4615384615 + -0.4615384615 = 0.0000000000
0.0000000000 + 2a + a2 = 0 + -0.4615384615
2a + a2 = 0 + -0.4615384615

Combine like terms: 0 + -0.4615384615 = -0.4615384615
2a + a2 = -0.4615384615

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 = -0.4615384615 + 1

Reorder the terms:
1 + 2a + a2 = -0.4615384615 + 1

Combine like terms: -0.4615384615 + 1 = 0.5384615385
1 + 2a + a2 = 0.5384615385

Factor a perfect square on the left side:
(a + 1)(a + 1) = 0.5384615385

Calculate the square root of the right side: 0.733799386

Break this problem into two subproblems by setting 
(a + 1) equal to 0.733799386 and -0.733799386.

Subproblem 1
a + 1 = 0.733799386

Simplifying
a + 1 = 0.733799386

Reorder the terms:
1 + a = 0.733799386

Solving
1 + a = 0.733799386

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 = 0.733799386 + -1

Combine like terms: 1 + -1 = 0
0 + a = 0.733799386 + -1
a = 0.733799386 + -1

Combine like terms: 0.733799386 + -1 = -0.266200614
a = -0.266200614

Simplifying
a = -0.266200614

Subproblem 2
a + 1 = -0.733799386

Simplifying
a + 1 = -0.733799386

Reorder the terms:
1 + a = -0.733799386

Solving
1 + a = -0.733799386

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 = -0.733799386 + -1

Combine like terms: 1 + -1 = 0
0 + a = -0.733799386 + -1
a = -0.733799386 + -1

Combine like terms: -0.733799386 + -1 = -1.733799386
a = -1.733799386

Simplifying
a = -1.733799386

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.266200614, -1.733799386}
Solution
a = {0, -0.266200614, -1.733799386}