(4a-3)(3a+1)=0

Solution for (4a-3)(3a+1)=0 equation:

Simplifying
(4a + -3)(3a + 1) = 0

Reorder the terms:
(-3 + 4a)(3a + 1) = 0

Reorder the terms:
(-3 + 4a)(1 + 3a) = 0

Multiply (-3 + 4a) * (1 + 3a)
(-3(1 + 3a) + 4a * (1 + 3a)) = 0
((1 * -3 + 3a * -3) + 4a * (1 + 3a)) = 0
((-3 + -9a) + 4a * (1 + 3a)) = 0
(-3 + -9a + (1 * 4a + 3a * 4a)) = 0
(-3 + -9a + (4a + 12a2)) = 0

Combine like terms: -9a + 4a = -5a
(-3 + -5a + 12a2) = 0

Solving
-3 + -5a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -3a)(3 + -4a) = 0

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

Simplifying
-1 + -3a = 0

Solving
-1 + -3a = 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 + -3a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3a = 0 + 1
-3a = 0 + 1

Combine like terms: 0 + 1 = 1
-3a = 1

Divide each side by '-3'.
a = -0.3333333333

Simplifying
a = -0.3333333333
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 = {-0.3333333333, 0.75}