(0.5t-2)(0.4t+6)=0

Solution for (0.5t-2)(0.4t+6)=0 equation:

Simplifying
(0.5t + -2)(0.4t + 6) = 0

Reorder the terms:
(-2 + 0.5t)(0.4t + 6) = 0

Reorder the terms:
(-2 + 0.5t)(6 + 0.4t) = 0

Multiply (-2 + 0.5t) * (6 + 0.4t)
(-2(6 + 0.4t) + 0.5t * (6 + 0.4t)) = 0
((6 * -2 + 0.4t * -2) + 0.5t * (6 + 0.4t)) = 0
((-12 + -0.8t) + 0.5t * (6 + 0.4t)) = 0
(-12 + -0.8t + (6 * 0.5t + 0.4t * 0.5t)) = 0
(-12 + -0.8t + (3t + 0.2t2)) = 0

Combine like terms: -0.8t + 3t = 2.2t
(-12 + 2.2t + 0.2t2) = 0

Solving
-12 + 2.2t + 0.2t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
0.2 the coefficient of the squared term: 

Divide each side by '0.2'.
-60 + 11t + t2 = 0

Move the constant term to the right:

Add '60' to each side of the equation.
-60 + 11t + 60 + t2 = 0 + 60

Reorder the terms:
-60 + 60 + 11t + t2 = 0 + 60

Combine like terms: -60 + 60 = 0
0 + 11t + t2 = 0 + 60
11t + t2 = 0 + 60

Combine like terms: 0 + 60 = 60
11t + t2 = 60

The t term is 11t.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11t + 30.25 + t2 = 60 + 30.25

Reorder the terms:
30.25 + 11t + t2 = 60 + 30.25

Combine like terms: 60 + 30.25 = 90.25
30.25 + 11t + t2 = 90.25

Factor a perfect square on the left side:
(t + 5.5)(t + 5.5) = 90.25

Calculate the square root of the right side: 9.5

Break this problem into two subproblems by setting 
(t + 5.5) equal to 9.5 and -9.5.

Subproblem 1
t + 5.5 = 9.5

Simplifying
t + 5.5 = 9.5

Reorder the terms:
5.5 + t = 9.5

Solving
5.5 + t = 9.5

Solving for variable 't'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + t = 9.5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + t = 9.5 + -5.5
t = 9.5 + -5.5

Combine like terms: 9.5 + -5.5 = 4
t = 4

Simplifying
t = 4

Subproblem 2
t + 5.5 = -9.5

Simplifying
t + 5.5 = -9.5

Reorder the terms:
5.5 + t = -9.5

Solving
5.5 + t = -9.5

Solving for variable 't'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + t = -9.5 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + t = -9.5 + -5.5
t = -9.5 + -5.5

Combine like terms: -9.5 + -5.5 = -15
t = -15

Simplifying
t = -15

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4, -15}