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

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

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

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

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

Multiply (-3 + 2t) * (4 + 3t)
3(-3(4 + 3t) + 2t * (4 + 3t)) = 0
3((4 * -3 + 3t * -3) + 2t * (4 + 3t)) = 0
3((-12 + -9t) + 2t * (4 + 3t)) = 0
3(-12 + -9t + (4 * 2t + 3t * 2t)) = 0
3(-12 + -9t + (8t + 6t2)) = 0

Combine like terms: -9t + 8t = -1t
3(-12 + -1t + 6t2) = 0
(-12 * 3 + -1t * 3 + 6t2 * 3) = 0
(-36 + -3t + 18t2) = 0

Solving
-36 + -3t + 18t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-12 + -1t + 6t2) = 0

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

Ignore the factor 3.
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 '(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 = {-1.333333333, 1.5}