(8t+5)(3t-9)=0

Solution for (8t+5)(3t-9)=0 equation:

Simplifying
(8t + 5)(3t + -9) = 0

Reorder the terms:
(5 + 8t)(3t + -9) = 0

Reorder the terms:
(5 + 8t)(-9 + 3t) = 0

Multiply (5 + 8t) * (-9 + 3t)
(5(-9 + 3t) + 8t * (-9 + 3t)) = 0
((-9 * 5 + 3t * 5) + 8t * (-9 + 3t)) = 0
((-45 + 15t) + 8t * (-9 + 3t)) = 0
(-45 + 15t + (-9 * 8t + 3t * 8t)) = 0
(-45 + 15t + (-72t + 24t2)) = 0

Combine like terms: 15t + -72t = -57t
(-45 + -57t + 24t2) = 0

Solving
-45 + -57t + 24t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + -19t + 8t2) = 0

Factor a trinomial.
3((-5 + -8t)(3 + -1t)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + -8t)' equal to zero and attempt to solve:

Simplifying
-5 + -8t = 0

Solving
-5 + -8t = 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 + -8t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -8t = 0 + 5
-8t = 0 + 5

Combine like terms: 0 + 5 = 5
-8t = 5

Divide each side by '-8'.
t = -0.625

Simplifying
t = -0.625
Subproblem 2
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
Solution
t = {-0.625, 3}