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

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

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

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

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

Multiply (-2 + 3t) * (-3 + t)
0 = (-2(-3 + t) + 3t * (-3 + t))
0 = ((-3 * -2 + t * -2) + 3t * (-3 + t))
0 = ((6 + -2t) + 3t * (-3 + t))
0 = (6 + -2t + (-3 * 3t + t * 3t))
0 = (6 + -2t + (-9t + 3t2))

Combine like terms: -2t + -9t = -11t
0 = (6 + -11t + 3t2)

Solving
0 = 6 + -11t + 3t2

Solving for variable 't'.

Combine like terms: 0 + -6 = -6
-6 + 11t + -3t2 = 6 + -11t + 3t2 + -6 + 11t + -3t2

Reorder the terms:
-6 + 11t + -3t2 = 6 + -6 + -11t + 11t + 3t2 + -3t2

Combine like terms: 6 + -6 = 0
-6 + 11t + -3t2 = 0 + -11t + 11t + 3t2 + -3t2
-6 + 11t + -3t2 = -11t + 11t + 3t2 + -3t2

Combine like terms: -11t + 11t = 0
-6 + 11t + -3t2 = 0 + 3t2 + -3t2
-6 + 11t + -3t2 = 3t2 + -3t2

Combine like terms: 3t2 + -3t2 = 0
-6 + 11t + -3t2 = 0

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

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

Simplifying
-3 + t = 0

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

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

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

Simplifying
t = 3
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 = {3, 0.6666666667}