(4a+3)(5a-3)=0

Solution for (4a+3)(5a-3)=0 equation:

Simplifying
(4a + 3)(5a + -3) = 0

Reorder the terms:
(3 + 4a)(5a + -3) = 0

Reorder the terms:
(3 + 4a)(-3 + 5a) = 0

Multiply (3 + 4a) * (-3 + 5a)
(3(-3 + 5a) + 4a * (-3 + 5a)) = 0
((-3 * 3 + 5a * 3) + 4a * (-3 + 5a)) = 0
((-9 + 15a) + 4a * (-3 + 5a)) = 0
(-9 + 15a + (-3 * 4a + 5a * 4a)) = 0
(-9 + 15a + (-12a + 20a2)) = 0

Combine like terms: 15a + -12a = 3a
(-9 + 3a + 20a2) = 0

Solving
-9 + 3a + 20a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -4a)(3 + -5a) = 0

Subproblem 1
Set the factor '(-3 + -4a)' equal to zero and attempt to solve:

Simplifying
-3 + -4a = 0

Solving
-3 + -4a = 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 + -4a = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4a = 0 + 3
-4a = 0 + 3

Combine like terms: 0 + 3 = 3
-4a = 3

Divide each side by '-4'.
a = -0.75

Simplifying
a = -0.75
Subproblem 2
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
Solution
a = {-0.75, 0.6}