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

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

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

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

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

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

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

Solving
-2 + -5a + 3a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -3a)(2 + -1a) = 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 '(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
Solution
a = {-0.3333333333, 2}