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

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

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

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

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

Multiply (5 + 3t) * (-4 + t)
(5(-4 + t) + 3t * (-4 + t)) = 0
((-4 * 5 + t * 5) + 3t * (-4 + t)) = 0
((-20 + 5t) + 3t * (-4 + t)) = 0
(-20 + 5t + (-4 * 3t + t * 3t)) = 0
(-20 + 5t + (-12t + 3t2)) = 0

Combine like terms: 5t + -12t = -7t
(-20 + -7t + 3t2) = 0

Solving
-20 + -7t + 3t2 = 0

Solving for variable 't'.

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

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

Simplifying
-5 + -3t = 0

Solving
-5 + -3t = 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 + -3t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -3t = 0 + 5
-3t = 0 + 5

Combine like terms: 0 + 5 = 5
-3t = 5

Divide each side by '-3'.
t = -1.666666667

Simplifying
t = -1.666666667
Subproblem 2
Set the factor '(4 + -1t)' equal to zero and attempt to solve:

Simplifying
4 + -1t = 0

Solving
4 + -1t = 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 + -1t = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1t = 0 + -4
-1t = 0 + -4

Combine like terms: 0 + -4 = -4
-1t = -4

Divide each side by '-1'.
t = 4

Simplifying
t = 4
Solution
t = {-1.666666667, 4}