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

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

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

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

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

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

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

Solving
-15 + 4t + 4t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-5 + -2t)(3 + -2t) = 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 '(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 = {-2.5, 1.5}