6(5a-1)(3a+1)=0

Solution for 6(5a-1)(3a+1)=0 equation:

Simplifying
6(5a + -1)(3a + 1) = 0

Reorder the terms:
6(-1 + 5a)(3a + 1) = 0

Reorder the terms:
6(-1 + 5a)(1 + 3a) = 0

Multiply (-1 + 5a) * (1 + 3a)
6(-1(1 + 3a) + 5a * (1 + 3a)) = 0
6((1 * -1 + 3a * -1) + 5a * (1 + 3a)) = 0
6((-1 + -3a) + 5a * (1 + 3a)) = 0
6(-1 + -3a + (1 * 5a + 3a * 5a)) = 0
6(-1 + -3a + (5a + 15a2)) = 0

Combine like terms: -3a + 5a = 2a
6(-1 + 2a + 15a2) = 0
(-1 * 6 + 2a * 6 + 15a2 * 6) = 0
(-6 + 12a + 90a2) = 0

Solving
-6 + 12a + 90a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 2a + 15a2) = 0

Factor a trinomial.
6((-1 + -3a)(1 + -5a)) = 0

Ignore the factor 6.
Subproblem 1
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
Subproblem 2
Set the factor '(1 + -5a)' equal to zero and attempt to solve:

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
Solution
a = {-0.3333333333, 0.2}