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

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

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

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

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

Multiply (-3 + 5t) * (5 + t)
(-3(5 + t) + 5t * (5 + t)) = 0
((5 * -3 + t * -3) + 5t * (5 + t)) = 0
((-15 + -3t) + 5t * (5 + t)) = 0
(-15 + -3t + (5 * 5t + t * 5t)) = 0
(-15 + -3t + (25t + 5t2)) = 0

Combine like terms: -3t + 25t = 22t
(-15 + 22t + 5t2) = 0

Solving
-15 + 22t + 5t2 = 0

Solving for variable 't'.

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

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

Simplifying
-5 + -1t = 0

Solving
-5 + -1t = 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 + -1t = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1t = 0 + 5
-1t = 0 + 5

Combine like terms: 0 + 5 = 5
-1t = 5

Divide each side by '-1'.
t = -5

Simplifying
t = -5
Subproblem 2
Set the factor '(3 + -5t)' equal to zero and attempt to solve:

Simplifying
3 + -5t = 0

Solving
3 + -5t = 0

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

Add '-3' to each side of the equation.
3 + -3 + -5t = 0 + -3

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

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

Divide each side by '-5'.
t = 0.6

Simplifying
t = 0.6
Solution
t = {-5, 0.6}