(4t-12)(5t-25)=0

Solution for (4t-12)(5t-25)=0 equation:

Simplifying
(4t + -12)(5t + -25) = 0

Reorder the terms:
(-12 + 4t)(5t + -25) = 0

Reorder the terms:
(-12 + 4t)(-25 + 5t) = 0

Multiply (-12 + 4t) * (-25 + 5t)
(-12(-25 + 5t) + 4t * (-25 + 5t)) = 0
((-25 * -12 + 5t * -12) + 4t * (-25 + 5t)) = 0
((300 + -60t) + 4t * (-25 + 5t)) = 0
(300 + -60t + (-25 * 4t + 5t * 4t)) = 0
(300 + -60t + (-100t + 20t2)) = 0

Combine like terms: -60t + -100t = -160t
(300 + -160t + 20t2) = 0

Solving
300 + -160t + 20t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '20'.
20(15 + -8t + t2) = 0

Factor a trinomial.
20((3 + -1t)(5 + -1t)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(3 + -1t)' equal to zero and attempt to solve:

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

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

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

Divide each side by '-1'.
t = 3

Simplifying
t = 3
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 = {3, 5}