2(3a+1)(6a-1)(-4)=

Solution for 2(3a+1)(6a-1)(-4)= equation:

Simplifying
2(3a + 1)(6a + -1)(-4) = 0

Reorder the terms:
2(1 + 3a)(6a + -1)(-4) = 0

Reorder the terms:
2(1 + 3a)(-1 + 6a)(-4) = 0

Reorder the terms for easier multiplication:
2 * -4(1 + 3a)(-1 + 6a) = 0

Multiply 2 * -4
-8(1 + 3a)(-1 + 6a) = 0

Multiply (1 + 3a) * (-1 + 6a)
-8(1(-1 + 6a) + 3a * (-1 + 6a)) = 0
-8((-1 * 1 + 6a * 1) + 3a * (-1 + 6a)) = 0
-8((-1 + 6a) + 3a * (-1 + 6a)) = 0
-8(-1 + 6a + (-1 * 3a + 6a * 3a)) = 0
-8(-1 + 6a + (-3a + 18a2)) = 0

Combine like terms: 6a + -3a = 3a
-8(-1 + 3a + 18a2) = 0
(-1 * -8 + 3a * -8 + 18a2 * -8) = 0
(8 + -24a + -144a2) = 0

Solving
8 + -24a + -144a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '8'.
8(1 + -3a + -18a2) = 0

Factor a trinomial.
8((1 + -6a)(1 + 3a)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(1 + -6a)' equal to zero and attempt to solve:

Simplifying
1 + -6a = 0

Solving
1 + -6a = 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 + -6a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -6a = 0 + -1
-6a = 0 + -1

Combine like terms: 0 + -1 = -1
-6a = -1

Divide each side by '-6'.
a = 0.1666666667

Simplifying
a = 0.1666666667
Subproblem 2
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 = {0.1666666667, -0.3333333333}