(3a-2)(4a+1)=

Solution for (3a-2)(4a+1)= equation:

Simplifying
(3a + -2)(4a + 1) = 0

Reorder the terms:
(-2 + 3a)(4a + 1) = 0

Reorder the terms:
(-2 + 3a)(1 + 4a) = 0

Multiply (-2 + 3a) * (1 + 4a)
(-2(1 + 4a) + 3a * (1 + 4a)) = 0
((1 * -2 + 4a * -2) + 3a * (1 + 4a)) = 0
((-2 + -8a) + 3a * (1 + 4a)) = 0
(-2 + -8a + (1 * 3a + 4a * 3a)) = 0
(-2 + -8a + (3a + 12a2)) = 0

Combine like terms: -8a + 3a = -5a
(-2 + -5a + 12a2) = 0

Solving
-2 + -5a + 12a2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-1 + -4a)(2 + -3a) = 0

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

Simplifying
-1 + -4a = 0

Solving
-1 + -4a = 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 + -4a = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4a = 0 + 1
-4a = 0 + 1

Combine like terms: 0 + 1 = 1
-4a = 1

Divide each side by '-4'.
a = -0.25

Simplifying
a = -0.25
Subproblem 2
Set the factor '(2 + -3a)' equal to zero and attempt to solve:

Simplifying
2 + -3a = 0

Solving
2 + -3a = 0

Move all terms containing a to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -3a = 0 + -2

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

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

Divide each side by '-3'.
a = 0.6666666667

Simplifying
a = 0.6666666667
Solution
a = {-0.25, 0.6666666667}