(4t+1)(3t-2)=0

Solution for (4t+1)(3t-2)=0 equation:

Simplifying
(4t + 1)(3t + -2) = 0

Reorder the terms:
(1 + 4t)(3t + -2) = 0

Reorder the terms:
(1 + 4t)(-2 + 3t) = 0

Multiply (1 + 4t) * (-2 + 3t)
(1(-2 + 3t) + 4t * (-2 + 3t)) = 0
((-2 * 1 + 3t * 1) + 4t * (-2 + 3t)) = 0
((-2 + 3t) + 4t * (-2 + 3t)) = 0
(-2 + 3t + (-2 * 4t + 3t * 4t)) = 0
(-2 + 3t + (-8t + 12t2)) = 0

Combine like terms: 3t + -8t = -5t
(-2 + -5t + 12t2) = 0

Solving
-2 + -5t + 12t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -4t)(2 + -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 '(2 + -3t)' equal to zero and attempt to solve:

Simplifying
2 + -3t = 0

Solving
2 + -3t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3t = 0 + -2
-3t = 0 + -2

Combine like terms: 0 + -2 = -2
-3t = -2

Divide each side by '-3'.
t = 0.6666666667

Simplifying
t = 0.6666666667
Solution
t = {-0.25, 0.6666666667}