(7a-1)(5a+3)=0

Solution for (7a-1)(5a+3)=0 equation:

Simplifying
(7a + -1)(5a + 3) = 0

Reorder the terms:
(-1 + 7a)(5a + 3) = 0

Reorder the terms:
(-1 + 7a)(3 + 5a) = 0

Multiply (-1 + 7a) * (3 + 5a)
(-1(3 + 5a) + 7a * (3 + 5a)) = 0
((3 * -1 + 5a * -1) + 7a * (3 + 5a)) = 0
((-3 + -5a) + 7a * (3 + 5a)) = 0
(-3 + -5a + (3 * 7a + 5a * 7a)) = 0
(-3 + -5a + (21a + 35a2)) = 0

Combine like terms: -5a + 21a = 16a
(-3 + 16a + 35a2) = 0

Solving
-3 + 16a + 35a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -5a)(1 + -7a) = 0

Subproblem 1
Set the factor '(-3 + -5a)' equal to zero and attempt to solve:

Simplifying
-3 + -5a = 0

Solving
-3 + -5a = 0

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

Add '3' to each side of the equation.
-3 + 3 + -5a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -5a = 0 + 3
-5a = 0 + 3

Combine like terms: 0 + 3 = 3
-5a = 3

Divide each side by '-5'.
a = -0.6

Simplifying
a = -0.6
Subproblem 2
Set the factor '(1 + -7a)' equal to zero and attempt to solve:

Simplifying
1 + -7a = 0

Solving
1 + -7a = 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 + -7a = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7a = 0 + -1
-7a = 0 + -1

Combine like terms: 0 + -1 = -1
-7a = -1

Divide each side by '-7'.
a = 0.1428571429

Simplifying
a = 0.1428571429
Solution
a = {-0.6, 0.1428571429}