(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 = 11a
(2 + 11a + 12a2) = 0

Solving
2 + 11a + 12a2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
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
Solution
a = {-0.6666666667, -0.25}