(5t-4)(t+9)=0

Solution for (5t-4)(t+9)=0 equation:

Simplifying
(5t + -4)(t + 9) = 0

Reorder the terms:
(-4 + 5t)(t + 9) = 0

Reorder the terms:
(-4 + 5t)(9 + t) = 0

Multiply (-4 + 5t) * (9 + t)
(-4(9 + t) + 5t * (9 + t)) = 0
((9 * -4 + t * -4) + 5t * (9 + t)) = 0
((-36 + -4t) + 5t * (9 + t)) = 0
(-36 + -4t + (9 * 5t + t * 5t)) = 0
(-36 + -4t + (45t + 5t2)) = 0

Combine like terms: -4t + 45t = 41t
(-36 + 41t + 5t2) = 0

Solving
-36 + 41t + 5t2 = 0

Solving for variable 't'.

Factor a trinomial.
(-9 + -1t)(4 + -5t) = 0

Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve:

Simplifying
-9 + -1t = 0

Solving
-9 + -1t = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1t = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1t = 0 + 9
-1t = 0 + 9

Combine like terms: 0 + 9 = 9
-1t = 9

Divide each side by '-1'.
t = -9

Simplifying
t = -9
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 = {-9, 0.8}