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

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

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

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

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

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

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

Solving
-12 + 1t + 6t2 = 0

Solving for variable 't'.

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {-1.5, 1.333333333}