(2t-5)(3t+4)=0

Solution for (2t-5)(3t+4)=0 equation:

Simplifying
(2t + -5)(3t + 4) = 0

Reorder the terms:
(-5 + 2t)(3t + 4) = 0

Reorder the terms:
(-5 + 2t)(4 + 3t) = 0

Multiply (-5 + 2t) * (4 + 3t)
(-5(4 + 3t) + 2t * (4 + 3t)) = 0
((4 * -5 + 3t * -5) + 2t * (4 + 3t)) = 0
((-20 + -15t) + 2t * (4 + 3t)) = 0
(-20 + -15t + (4 * 2t + 3t * 2t)) = 0
(-20 + -15t + (8t + 6t2)) = 0

Combine like terms: -15t + 8t = -7t
(-20 + -7t + 6t2) = 0

Solving
-20 + -7t + 6t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-4 + -3t)(5 + -2t) = 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 '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {-1.333333333, 2.5}