10=0.25(t-5)(t-1)

Solution for 10=0.25(t-5)(t-1) equation:

Simplifying
10 = 0.25(t + -5)(t + -1)

Reorder the terms:
10 = 0.25(-5 + t)(t + -1)

Reorder the terms:
10 = 0.25(-5 + t)(-1 + t)

Multiply (-5 + t) * (-1 + t)
10 = 0.25(-5(-1 + t) + t(-1 + t))
10 = 0.25((-1 * -5 + t * -5) + t(-1 + t))
10 = 0.25((5 + -5t) + t(-1 + t))
10 = 0.25(5 + -5t + (-1 * t + t * t))
10 = 0.25(5 + -5t + (-1t + t2))

Combine like terms: -5t + -1t = -6t
10 = 0.25(5 + -6t + t2)
10 = (5 * 0.25 + -6t * 0.25 + t2 * 0.25)
10 = (1.25 + -1.5t + 0.25t2)

Solving
10 = 1.25 + -1.5t + 0.25t2

Solving for variable 't'.

Combine like terms: 10 + -1.25 = 8.75
8.75 + 1.5t + -0.25t2 = 1.25 + -1.5t + 0.25t2 + -1.25 + 1.5t + -0.25t2

Reorder the terms:
8.75 + 1.5t + -0.25t2 = 1.25 + -1.25 + -1.5t + 1.5t + 0.25t2 + -0.25t2

Combine like terms: 1.25 + -1.25 = 0.00
8.75 + 1.5t + -0.25t2 = 0.00 + -1.5t + 1.5t + 0.25t2 + -0.25t2
8.75 + 1.5t + -0.25t2 = -1.5t + 1.5t + 0.25t2 + -0.25t2

Combine like terms: -1.5t + 1.5t = 0.0
8.75 + 1.5t + -0.25t2 = 0.0 + 0.25t2 + -0.25t2
8.75 + 1.5t + -0.25t2 = 0.25t2 + -0.25t2

Combine like terms: 0.25t2 + -0.25t2 = 0.00
8.75 + 1.5t + -0.25t2 = 0.00

Begin completing the square.  Divide all terms by
-0.25 the coefficient of the squared term: 

Divide each side by '-0.25'.
-35 + -6t + t2 = 0

Move the constant term to the right:

Add '35' to each side of the equation.
-35 + -6t + 35 + t2 = 0 + 35

Reorder the terms:
-35 + 35 + -6t + t2 = 0 + 35

Combine like terms: -35 + 35 = 0
0 + -6t + t2 = 0 + 35
-6t + t2 = 0 + 35

Combine like terms: 0 + 35 = 35
-6t + t2 = 35

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 35 + 9

Reorder the terms:
9 + -6t + t2 = 35 + 9

Combine like terms: 35 + 9 = 44
9 + -6t + t2 = 44

Factor a perfect square on the left side:
(t + -3)(t + -3) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(t + -3) equal to 6.633249581 and -6.633249581.

Subproblem 1
t + -3 = 6.633249581

Simplifying
t + -3 = 6.633249581

Reorder the terms:
-3 + t = 6.633249581

Solving
-3 + t = 6.633249581

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 6.633249581 + 3

Combine like terms: -3 + 3 = 0
0 + t = 6.633249581 + 3
t = 6.633249581 + 3

Combine like terms: 6.633249581 + 3 = 9.633249581
t = 9.633249581

Simplifying
t = 9.633249581

Subproblem 2
t + -3 = -6.633249581

Simplifying
t + -3 = -6.633249581

Reorder the terms:
-3 + t = -6.633249581

Solving
-3 + t = -6.633249581

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -6.633249581 + 3

Combine like terms: -3 + 3 = 0
0 + t = -6.633249581 + 3
t = -6.633249581 + 3

Combine like terms: -6.633249581 + 3 = -3.633249581
t = -3.633249581

Simplifying
t = -3.633249581

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.633249581, -3.633249581}