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

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

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

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

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

Multiply (-3 + 4t) * (-2 + t)
(-3(-2 + t) + 4t * (-2 + t)) = 0
((-2 * -3 + t * -3) + 4t * (-2 + t)) = 0
((6 + -3t) + 4t * (-2 + t)) = 0
(6 + -3t + (-2 * 4t + t * 4t)) = 0
(6 + -3t + (-8t + 4t2)) = 0

Combine like terms: -3t + -8t = -11t
(6 + -11t + 4t2) = 0

Solving
6 + -11t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(3 + -4t)(2 + -1t) = 0

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

Simplifying
3 + -4t = 0

Solving
3 + -4t = 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 + -4t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4t = 0 + -3
-4t = 0 + -3

Combine like terms: 0 + -3 = -3
-4t = -3

Divide each side by '-4'.
t = 0.75

Simplifying
t = 0.75
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 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 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {0.75, 2}