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

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

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

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

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

Multiply (-5 + 6a) * (1 + 3a)
(-5(1 + 3a) + 6a * (1 + 3a)) = 0
((1 * -5 + 3a * -5) + 6a * (1 + 3a)) = 0
((-5 + -15a) + 6a * (1 + 3a)) = 0
(-5 + -15a + (1 * 6a + 3a * 6a)) = 0
(-5 + -15a + (6a + 18a2)) = 0

Combine like terms: -15a + 6a = -9a
(-5 + -9a + 18a2) = 0

Solving
-5 + -9a + 18a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -3a)(5 + -6a) = 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 '(5 + -6a)' equal to zero and attempt to solve:

Simplifying
5 + -6a = 0

Solving
5 + -6a = 0

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

Add '-5' to each side of the equation.
5 + -5 + -6a = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -6a = 0 + -5
-6a = 0 + -5

Combine like terms: 0 + -5 = -5
-6a = -5

Divide each side by '-6'.
a = 0.8333333333

Simplifying
a = 0.8333333333
Solution
a = {-0.3333333333, 0.8333333333}