2(t+5)(t-8)=0

Solution for 2(t+5)(t-8)=0 equation:

Simplifying
2(t + 5)(t + -8) = 0

Reorder the terms:
2(5 + t)(t + -8) = 0

Reorder the terms:
2(5 + t)(-8 + t) = 0

Multiply (5 + t) * (-8 + t)
2(5(-8 + t) + t(-8 + t)) = 0
2((-8 * 5 + t * 5) + t(-8 + t)) = 0
2((-40 + 5t) + t(-8 + t)) = 0
2(-40 + 5t + (-8 * t + t * t)) = 0
2(-40 + 5t + (-8t + t2)) = 0

Combine like terms: 5t + -8t = -3t
2(-40 + -3t + t2) = 0
(-40 * 2 + -3t * 2 + t2 * 2) = 0
(-80 + -6t + 2t2) = 0

Solving
-80 + -6t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-40 + -3t + t2) = 0

Factor a trinomial.
2((-5 + -1t)(8 + -1t)) = 0

Ignore the factor 2.
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 '(8 + -1t)' equal to zero and attempt to solve:

Simplifying
8 + -1t = 0

Solving
8 + -1t = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1t = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1t = 0 + -8
-1t = 0 + -8

Combine like terms: 0 + -8 = -8
-1t = -8

Divide each side by '-1'.
t = 8

Simplifying
t = 8
Solution
t = {-5, 8}