(4t+5)(3t+10)=0

Solution for (4t+5)(3t+10)=0 equation:

Simplifying
(4t + 5)(3t + 10) = 0

Reorder the terms:
(5 + 4t)(3t + 10) = 0

Reorder the terms:
(5 + 4t)(10 + 3t) = 0

Multiply (5 + 4t) * (10 + 3t)
(5(10 + 3t) + 4t * (10 + 3t)) = 0
((10 * 5 + 3t * 5) + 4t * (10 + 3t)) = 0
((50 + 15t) + 4t * (10 + 3t)) = 0
(50 + 15t + (10 * 4t + 3t * 4t)) = 0
(50 + 15t + (40t + 12t2)) = 0

Combine like terms: 15t + 40t = 55t
(50 + 55t + 12t2) = 0

Solving
50 + 55t + 12t2 = 0

Solving for variable 't'.

Factor a trinomial.
(10 + 3t)(5 + 4t) = 0

Subproblem 1
Set the factor '(10 + 3t)' equal to zero and attempt to solve:

Simplifying
10 + 3t = 0

Solving
10 + 3t = 0

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

Add '-10' to each side of the equation.
10 + -10 + 3t = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 3t = 0 + -10
3t = 0 + -10

Combine like terms: 0 + -10 = -10
3t = -10

Divide each side by '3'.
t = -3.333333333

Simplifying
t = -3.333333333
Subproblem 2
Set the factor '(5 + 4t)' equal to zero and attempt to solve:

Simplifying
5 + 4t = 0

Solving
5 + 4t = 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 + 4t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4t = 0 + -5
4t = 0 + -5

Combine like terms: 0 + -5 = -5
4t = -5

Divide each side by '4'.
t = -1.25

Simplifying
t = -1.25
Solution
t = {-3.333333333, -1.25}