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

Subproblem 1
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
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 = {-2.5, 1.333333333}