(3t+1)(4t-5)=

Solution for (3t+1)(4t-5)= equation:

Simplifying
(3t + 1)(4t + -5) = 0

Reorder the terms:
(1 + 3t)(4t + -5) = 0

Reorder the terms:
(1 + 3t)(-5 + 4t) = 0

Multiply (1 + 3t) * (-5 + 4t)
(1(-5 + 4t) + 3t * (-5 + 4t)) = 0
((-5 * 1 + 4t * 1) + 3t * (-5 + 4t)) = 0
((-5 + 4t) + 3t * (-5 + 4t)) = 0
(-5 + 4t + (-5 * 3t + 4t * 3t)) = 0
(-5 + 4t + (-15t + 12t2)) = 0

Combine like terms: 4t + -15t = -11t
(-5 + -11t + 12t2) = 0

Solving
-5 + -11t + 12t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-1 + -3t)(5 + -4t) = 0

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

Simplifying
-1 + -3t = 0

Solving
-1 + -3t = 0

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

Add '1' to each side of the equation.
-1 + 1 + -3t = 0 + 1

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

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

Divide each side by '-3'.
t = -0.3333333333

Simplifying
t = -0.3333333333
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 = {-0.3333333333, 1.25}