(5t-10)(4t+24)=0

Solution for (5t-10)(4t+24)=0 equation:

Simplifying
(5t + -10)(4t + 24) = 0

Reorder the terms:
(-10 + 5t)(4t + 24) = 0

Reorder the terms:
(-10 + 5t)(24 + 4t) = 0

Multiply (-10 + 5t) * (24 + 4t)
(-10(24 + 4t) + 5t * (24 + 4t)) = 0
((24 * -10 + 4t * -10) + 5t * (24 + 4t)) = 0
((-240 + -40t) + 5t * (24 + 4t)) = 0
(-240 + -40t + (24 * 5t + 4t * 5t)) = 0
(-240 + -40t + (120t + 20t2)) = 0

Combine like terms: -40t + 120t = 80t
(-240 + 80t + 20t2) = 0

Solving
-240 + 80t + 20t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '20'.
20(-12 + 4t + t2) = 0

Factor a trinomial.
20((-6 + -1t)(2 + -1t)) = 0

Ignore the factor 20.
Subproblem 1
Set the factor '(-6 + -1t)' equal to zero and attempt to solve:

Simplifying
-6 + -1t = 0

Solving
-6 + -1t = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1t = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1t = 0 + 6
-1t = 0 + 6

Combine like terms: 0 + 6 = 6
-1t = 6

Divide each side by '-1'.
t = -6

Simplifying
t = -6
Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve:

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
Solution
t = {-6, 2}