(7t+6)(5t+4)=0

Solution for (7t+6)(5t+4)=0 equation:

Simplifying
(7t + 6)(5t + 4) = 0

Reorder the terms:
(6 + 7t)(5t + 4) = 0

Reorder the terms:
(6 + 7t)(4 + 5t) = 0

Multiply (6 + 7t) * (4 + 5t)
(6(4 + 5t) + 7t * (4 + 5t)) = 0
((4 * 6 + 5t * 6) + 7t * (4 + 5t)) = 0
((24 + 30t) + 7t * (4 + 5t)) = 0
(24 + 30t + (4 * 7t + 5t * 7t)) = 0
(24 + 30t + (28t + 35t2)) = 0

Combine like terms: 30t + 28t = 58t
(24 + 58t + 35t2) = 0

Solving
24 + 58t + 35t2 = 0

Solving for variable 't'.

Factor a trinomial.
(6 + 7t)(4 + 5t) = 0

Subproblem 1
Set the factor '(6 + 7t)' equal to zero and attempt to solve:

Simplifying
6 + 7t = 0

Solving
6 + 7t = 0

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

Add '-6' to each side of the equation.
6 + -6 + 7t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 7t = 0 + -6
7t = 0 + -6

Combine like terms: 0 + -6 = -6
7t = -6

Divide each side by '7'.
t = -0.8571428571

Simplifying
t = -0.8571428571
Subproblem 2
Set the factor '(4 + 5t)' equal to zero and attempt to solve:

Simplifying
4 + 5t = 0

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

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

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

Divide each side by '5'.
t = -0.8

Simplifying
t = -0.8
Solution
t = {-0.8571428571, -0.8}