(5a+2)(3a-1)=0

Solution for (5a+2)(3a-1)=0 equation:

Simplifying
(5a + 2)(3a + -1) = 0

Reorder the terms:
(2 + 5a)(3a + -1) = 0

Reorder the terms:
(2 + 5a)(-1 + 3a) = 0

Multiply (2 + 5a) * (-1 + 3a)
(2(-1 + 3a) + 5a * (-1 + 3a)) = 0
((-1 * 2 + 3a * 2) + 5a * (-1 + 3a)) = 0
((-2 + 6a) + 5a * (-1 + 3a)) = 0
(-2 + 6a + (-1 * 5a + 3a * 5a)) = 0
(-2 + 6a + (-5a + 15a2)) = 0

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

Solving
-2 + 1a + 15a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-2 + -5a)(1 + -3a) = 0

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

Simplifying
-2 + -5a = 0

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

Combine like terms: -2 + 2 = 0
0 + -5a = 0 + 2
-5a = 0 + 2

Combine like terms: 0 + 2 = 2
-5a = 2

Divide each side by '-5'.
a = -0.4

Simplifying
a = -0.4
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 = {-0.4, 0.3333333333}