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

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

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

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

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

Multiply (-2 + 5t) * (-3 + 2t)
(-2(-3 + 2t) + 5t * (-3 + 2t)) = 0
((-3 * -2 + 2t * -2) + 5t * (-3 + 2t)) = 0
((6 + -4t) + 5t * (-3 + 2t)) = 0
(6 + -4t + (-3 * 5t + 2t * 5t)) = 0
(6 + -4t + (-15t + 10t2)) = 0

Combine like terms: -4t + -15t = -19t
(6 + -19t + 10t2) = 0

Solving
6 + -19t + 10t2 = 0

Solving for variable 't'.

Factor a trinomial.
(2 + -5t)(3 + -2t) = 0

Subproblem 1
Set the factor '(2 + -5t)' equal to zero and attempt to solve:

Simplifying
2 + -5t = 0

Solving
2 + -5t = 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 + -5t = 0 + -2

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

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

Divide each side by '-5'.
t = 0.4

Simplifying
t = 0.4
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 = {0.4, 1.5}