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

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

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

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

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

Combine like terms: 12t + -1t = 11t
(4 + 11t + -3t2) = 0

Solving
4 + 11t + -3t2 = 0

Solving for variable 't'.

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

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

Simplifying
4 + -1t = 0

Solving
4 + -1t = 0

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

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

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

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

Divide each side by '-1'.
t = 4

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

Simplifying
1 + 3t = 0

Solving
1 + 3t = 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 + 3t = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3t = 0 + -1
3t = 0 + -1

Combine like terms: 0 + -1 = -1
3t = -1

Divide each side by '3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
Solution
t = {4, -0.3333333333}