(3t-4)(t-6)=0

Solution for (3t-4)(t-6)=0 equation:

Simplifying
(3t + -4)(t + -6) = 0

Reorder the terms:
(-4 + 3t)(t + -6) = 0

Reorder the terms:
(-4 + 3t)(-6 + t) = 0

Multiply (-4 + 3t) * (-6 + t)
(-4(-6 + t) + 3t * (-6 + t)) = 0
((-6 * -4 + t * -4) + 3t * (-6 + t)) = 0
((24 + -4t) + 3t * (-6 + t)) = 0
(24 + -4t + (-6 * 3t + t * 3t)) = 0
(24 + -4t + (-18t + 3t2)) = 0

Combine like terms: -4t + -18t = -22t
(24 + -22t + 3t2) = 0

Solving
24 + -22t + 3t2 = 0

Solving for variable 't'.

Factor a trinomial.
(4 + -3t)(6 + -1t) = 0

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

Simplifying
4 + -3t = 0

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

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

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

Divide each side by '-3'.
t = 1.333333333

Simplifying
t = 1.333333333
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {1.333333333, 6}