(5a-2)(7a+3)=0

Solution for (5a-2)(7a+3)=0 equation:

Simplifying
(5a + -2)(7a + 3) = 0

Reorder the terms:
(-2 + 5a)(7a + 3) = 0

Reorder the terms:
(-2 + 5a)(3 + 7a) = 0

Multiply (-2 + 5a) * (3 + 7a)
(-2(3 + 7a) + 5a * (3 + 7a)) = 0
((3 * -2 + 7a * -2) + 5a * (3 + 7a)) = 0
((-6 + -14a) + 5a * (3 + 7a)) = 0
(-6 + -14a + (3 * 5a + 7a * 5a)) = 0
(-6 + -14a + (15a + 35a2)) = 0

Combine like terms: -14a + 15a = 1a
(-6 + 1a + 35a2) = 0

Solving
-6 + 1a + 35a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -7a)(2 + -5a) = 0

Subproblem 1
Set the factor '(-3 + -7a)' equal to zero and attempt to solve:

Simplifying
-3 + -7a = 0

Solving
-3 + -7a = 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 + -7a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -7a = 0 + 3
-7a = 0 + 3

Combine like terms: 0 + 3 = 3
-7a = 3

Divide each side by '-7'.
a = -0.4285714286

Simplifying
a = -0.4285714286
Subproblem 2
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
Solution
a = {-0.4285714286, 0.4}