10=20t-5t(-5t)

Solution for 10=20t-5t(-5t) equation:

Simplifying
10 = 20t + -5t(-5t)

Remove parenthesis around (-5t)
10 = 20t + -5t * -5t

Reorder the terms for easier multiplication:
10 = 20t + -5 * -5t * t

Multiply -5 * -5
10 = 20t + 25t * t

Multiply t * t
10 = 20t + 25t2

Solving
10 = 20t + 25t2

Solving for variable 't'.

Reorder the terms:
10 + -20t + -25t2 = 20t + -20t + 25t2 + -25t2

Combine like terms: 20t + -20t = 0
10 + -20t + -25t2 = 0 + 25t2 + -25t2
10 + -20t + -25t2 = 25t2 + -25t2

Combine like terms: 25t2 + -25t2 = 0
10 + -20t + -25t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(2 + -4t + -5t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(2 + -4t + -5t2)' equal to zero and attempt to solve:

Simplifying
2 + -4t + -5t2 = 0

Solving
2 + -4t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + 0.8t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + 0.8t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + 0.8t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + 0.8t + t2 = 0 + 0.4
0.8t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
0.8t + t2 = 0.4

The t term is 0.8t.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8t + 0.16 + t2 = 0.4 + 0.16

Reorder the terms:
0.16 + 0.8t + t2 = 0.4 + 0.16

Combine like terms: 0.4 + 0.16 = 0.56
0.16 + 0.8t + t2 = 0.56

Factor a perfect square on the left side:
(t + 0.4)(t + 0.4) = 0.56

Calculate the square root of the right side: 0.748331477

Break this problem into two subproblems by setting 
(t + 0.4) equal to 0.748331477 and -0.748331477.

Subproblem 1
t + 0.4 = 0.748331477

Simplifying
t + 0.4 = 0.748331477

Reorder the terms:
0.4 + t = 0.748331477

Solving
0.4 + t = 0.748331477

Solving for variable 't'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + t = 0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + t = 0.748331477 + -0.4
t = 0.748331477 + -0.4

Combine like terms: 0.748331477 + -0.4 = 0.348331477
t = 0.348331477

Simplifying
t = 0.348331477

Subproblem 2
t + 0.4 = -0.748331477

Simplifying
t + 0.4 = -0.748331477

Reorder the terms:
0.4 + t = -0.748331477

Solving
0.4 + t = -0.748331477

Solving for variable 't'.

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

Add '-0.4' to each side of the equation.
0.4 + -0.4 + t = -0.748331477 + -0.4

Combine like terms: 0.4 + -0.4 = 0.0
0.0 + t = -0.748331477 + -0.4
t = -0.748331477 + -0.4

Combine like terms: -0.748331477 + -0.4 = -1.148331477
t = -1.148331477

Simplifying
t = -1.148331477

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.348331477, -1.148331477}
Solution
t = {0.348331477, -1.148331477}