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

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

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

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

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

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

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

Solving
-3 + 5a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3 + -4a)(1 + -3a) = 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 '(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
Solution
a = {-0.75, 0.3333333333}