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

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

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

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

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

Multiply (-5 + 3a) * (3 + 2a)
(-5(3 + 2a) + 3a * (3 + 2a)) = 0
((3 * -5 + 2a * -5) + 3a * (3 + 2a)) = 0
((-15 + -10a) + 3a * (3 + 2a)) = 0
(-15 + -10a + (3 * 3a + 2a * 3a)) = 0
(-15 + -10a + (9a + 6a2)) = 0

Combine like terms: -10a + 9a = -1a
(-15 + -1a + 6a2) = 0

Solving
-15 + -1a + 6a2 = 0

Solving for variable 'a'.

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

Subproblem 1
Set the factor '(-3 + -2a)' equal to zero and attempt to solve:

Simplifying
-3 + -2a = 0

Solving
-3 + -2a = 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 + -2a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2a = 0 + 3
-2a = 0 + 3

Combine like terms: 0 + 3 = 3
-2a = 3

Divide each side by '-2'.
a = -1.5

Simplifying
a = -1.5
Subproblem 2
Set the factor '(5 + -3a)' equal to zero and attempt to solve:

Simplifying
5 + -3a = 0

Solving
5 + -3a = 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 + -3a = 0 + -5

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

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

Divide each side by '-3'.
a = 1.666666667

Simplifying
a = 1.666666667
Solution
a = {-1.5, 1.666666667}