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

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

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

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

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

Multiply (-5 + 2t) * (2 + t)
2(-5(2 + t) + 2t * (2 + t)) = 0
2((2 * -5 + t * -5) + 2t * (2 + t)) = 0
2((-10 + -5t) + 2t * (2 + t)) = 0
2(-10 + -5t + (2 * 2t + t * 2t)) = 0
2(-10 + -5t + (4t + 2t2)) = 0

Combine like terms: -5t + 4t = -1t
2(-10 + -1t + 2t2) = 0
(-10 * 2 + -1t * 2 + 2t2 * 2) = 0
(-20 + -2t + 4t2) = 0

Solving
-20 + -2t + 4t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + -1t + 2t2) = 0

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

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(5 + -2t)' equal to zero and attempt to solve:

Simplifying
5 + -2t = 0

Solving
5 + -2t = 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 + -2t = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2t = 0 + -5
-2t = 0 + -5

Combine like terms: 0 + -5 = -5
-2t = -5

Divide each side by '-2'.
t = 2.5

Simplifying
t = 2.5
Solution
t = {-2, 2.5}