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

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

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

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

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

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

Combine like terms: 2a + -3a = -1a
(-1 + -1a + 6a2) = 0

Solving
-1 + -1a + 6a2 = 0

Solving for variable 'a'.

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

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 + -2a)' equal to zero and attempt to solve:

Simplifying
1 + -2a = 0

Solving
1 + -2a = 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 + -2a = 0 + -1

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

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

Divide each side by '-2'.
a = 0.5

Simplifying
a = 0.5
Solution
a = {-0.3333333333, 0.5}