25t^2-25t-500=0

Solution for 25t^2-25t-500=0 equation:

Simplifying
25t2 + -25t + -500 = 0

Reorder the terms:
-500 + -25t + 25t2 = 0

Solving
-500 + -25t + 25t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '25'.
25(-20 + -1t + t2) = 0

Factor a trinomial.
25((-4 + -1t)(5 + -1t)) = 0

Ignore the factor 25.
Subproblem 1
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
Subproblem 2
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
Solution
t = {-4, 5}