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

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

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

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

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

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

Combine like terms: 2t + -12t = -10t
(-3 + -10t + 8t2) = 0

Solving
-3 + -10t + 8t2 = 0

Solving for variable 't'.

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

Simplifying
3 + -2t = 0

Solving
3 + -2t = 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 + -2t = 0 + -3

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

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

Divide each side by '-2'.
t = 1.5

Simplifying
t = 1.5
Solution
t = {-0.25, 1.5}