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

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

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

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

Combine like terms: -5a + -3a = -8a
(1 + -8a + 15a2) = 0

Solving
1 + -8a + 15a2 = 0

Solving for variable 'a'.

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

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

Simplifying
1 + -5a = 0

Solving
1 + -5a = 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 + -5a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5a = 0 + -1
-5a = 0 + -1

Combine like terms: 0 + -1 = -1
-5a = -1

Divide each side by '-5'.
a = 0.2

Simplifying
a = 0.2
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 = {0.2, 0.3333333333}