(4t+1)(t+3)=

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

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

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

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

Multiply (1 + 4t) * (3 + t)
(1(3 + t) + 4t * (3 + t)) = 0
((3 * 1 + t * 1) + 4t * (3 + t)) = 0
((3 + 1t) + 4t * (3 + t)) = 0
(3 + 1t + (3 * 4t + t * 4t)) = 0
(3 + 1t + (12t + 4t2)) = 0

Combine like terms: 1t + 12t = 13t
(3 + 13t + 4t2) = 0

Solving
3 + 13t + 4t2 = 0

Solving for variable 't'.

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

Subproblem 1
Set the factor '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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

Add '-3' to each side of the equation.
3 + -3 + t = 0 + -3

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

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

Simplifying
t = -3
Subproblem 2
Set the factor '(1 + 4t)' equal to zero and attempt to solve:

Simplifying
1 + 4t = 0

Solving
1 + 4t = 0

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

Add '-1' to each side of the equation.
1 + -1 + 4t = 0 + -1

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

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

Divide each side by '4'.
t = -0.25

Simplifying
t = -0.25
Solution
t = {-3, -0.25}