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

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

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

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

Combine like terms: -2a + 15a = 13a
(5 + 13a + -6a2) = 0

Solving
5 + 13a + -6a2 = 0

Solving for variable 'a'.

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

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

Simplifying
5 + -2a = 0

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

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

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

Divide each side by '-2'.
a = 2.5

Simplifying
a = 2.5
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 = {2.5, -0.3333333333}