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

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

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

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

Remove parenthesis around (1 + 3t)
1 + 3t + -4t(3t + 1) = 0

Reorder the terms:
1 + 3t + -4t(1 + 3t) = 0
1 + 3t + (1 * -4t + 3t * -4t) = 0
1 + 3t + (-4t + -12t2) = 0

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

Solving
1 + -1t + -12t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
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 = {0.25, -0.3333333333}