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

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

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

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

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

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

Combine like terms: 1a + 12a = 13a
(3 + 13a + 4a2) = 0

Solving
3 + 13a + 4a2 = 0

Solving for variable 'a'.

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

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

Simplifying
3 + a = 0

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

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

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

Simplifying
a = -3
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 = {-3, -0.25}