(4a-3)(6a+5)=0

Solution for (4a-3)(6a+5)=0 equation:

Simplifying
(4a + -3)(6a + 5) = 0

Reorder the terms:
(-3 + 4a)(6a + 5) = 0

Reorder the terms:
(-3 + 4a)(5 + 6a) = 0

Multiply (-3 + 4a) * (5 + 6a)
(-3(5 + 6a) + 4a * (5 + 6a)) = 0
((5 * -3 + 6a * -3) + 4a * (5 + 6a)) = 0
((-15 + -18a) + 4a * (5 + 6a)) = 0
(-15 + -18a + (5 * 4a + 6a * 4a)) = 0
(-15 + -18a + (20a + 24a2)) = 0

Combine like terms: -18a + 20a = 2a
(-15 + 2a + 24a2) = 0

Solving
-15 + 2a + 24a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-5 + -6a)(3 + -4a) = 0

Subproblem 1
Set the factor '(-5 + -6a)' equal to zero and attempt to solve:

Simplifying
-5 + -6a = 0

Solving
-5 + -6a = 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 + -6a = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -6a = 0 + 5
-6a = 0 + 5

Combine like terms: 0 + 5 = 5
-6a = 5

Divide each side by '-6'.
a = -0.8333333333

Simplifying
a = -0.8333333333
Subproblem 2
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
Solution
a = {-0.8333333333, 0.75}