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

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

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

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

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

Combine like terms: -9t + 2t = -7t
(-6 + -7t + 3t2) = 0

Solving
-6 + -7t + 3t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.6666666667, 3}