5a(3a-1)(2a+4)=0

Solution for 5a(3a-1)(2a+4)=0 equation:

Simplifying
5a(3a + -1)(2a + 4) = 0

Reorder the terms:
5a(-1 + 3a)(2a + 4) = 0

Reorder the terms:
5a(-1 + 3a)(4 + 2a) = 0

Multiply (-1 + 3a) * (4 + 2a)
5a(-1(4 + 2a) + 3a * (4 + 2a)) = 0
5a((4 * -1 + 2a * -1) + 3a * (4 + 2a)) = 0
5a((-4 + -2a) + 3a * (4 + 2a)) = 0
5a(-4 + -2a + (4 * 3a + 2a * 3a)) = 0
5a(-4 + -2a + (12a + 6a2)) = 0

Combine like terms: -2a + 12a = 10a
5a(-4 + 10a + 6a2) = 0
(-4 * 5a + 10a * 5a + 6a2 * 5a) = 0
(-20a + 50a2 + 30a3) = 0

Solving
-20a + 50a2 + 30a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '10a'.
10a(-2 + 5a + 3a2) = 0

Factor a trinomial.
10a((-2 + -1a)(1 + -3a)) = 0

Ignore the factor 10.
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 '(-2 + -1a)' equal to zero and attempt to solve:

Simplifying
-2 + -1a = 0

Solving
-2 + -1a = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1a = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1a = 0 + 2
-1a = 0 + 2

Combine like terms: 0 + 2 = 2
-1a = 2

Divide each side by '-1'.
a = -2

Simplifying
a = -2
Subproblem 3
Set the factor '(1 + -3a)' equal to zero and attempt to solve:

Simplifying
1 + -3a = 0

Solving
1 + -3a = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3a = 0 + -1
-3a = 0 + -1

Combine like terms: 0 + -1 = -1
-3a = -1

Divide each side by '-3'.
a = 0.3333333333

Simplifying
a = 0.3333333333
Solution
a = {0, -2, 0.3333333333}