5t(2t-5)=50-5t

Solution for 5t(2t-5)=50-5t equation:

Simplifying
5t(2t + -5) = 50 + -5t

Reorder the terms:
5t(-5 + 2t) = 50 + -5t
(-5 * 5t + 2t * 5t) = 50 + -5t
(-25t + 10t2) = 50 + -5t

Solving
-25t + 10t2 = 50 + -5t

Solving for variable 't'.

Reorder the terms:
-50 + -25t + 5t + 10t2 = 50 + -5t + -50 + 5t

Combine like terms: -25t + 5t = -20t
-50 + -20t + 10t2 = 50 + -5t + -50 + 5t

Reorder the terms:
-50 + -20t + 10t2 = 50 + -50 + -5t + 5t

Combine like terms: 50 + -50 = 0
-50 + -20t + 10t2 = 0 + -5t + 5t
-50 + -20t + 10t2 = -5t + 5t

Combine like terms: -5t + 5t = 0
-50 + -20t + 10t2 = 0

Factor out the Greatest Common Factor (GCF), '10'.
10(-5 + -2t + t2) = 0

Ignore the factor 10.
Subproblem 1
Set the factor '(-5 + -2t + t2)' equal to zero and attempt to solve:

Simplifying
-5 + -2t + t2 = 0

Solving
-5 + -2t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + -2t + 5 + t2 = 0 + 5

Reorder the terms:
-5 + 5 + -2t + t2 = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -2t + t2 = 0 + 5
-2t + t2 = 0 + 5

Combine like terms: 0 + 5 = 5
-2t + t2 = 5

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 5 + 1

Reorder the terms:
1 + -2t + t2 = 5 + 1

Combine like terms: 5 + 1 = 6
1 + -2t + t2 = 6

Factor a perfect square on the left side:
(t + -1)(t + -1) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(t + -1) equal to 2.449489743 and -2.449489743.

Subproblem 1
t + -1 = 2.449489743

Simplifying
t + -1 = 2.449489743

Reorder the terms:
-1 + t = 2.449489743

Solving
-1 + t = 2.449489743

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = 2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + t = 2.449489743 + 1
t = 2.449489743 + 1

Combine like terms: 2.449489743 + 1 = 3.449489743
t = 3.449489743

Simplifying
t = 3.449489743

Subproblem 2
t + -1 = -2.449489743

Simplifying
t + -1 = -2.449489743

Reorder the terms:
-1 + t = -2.449489743

Solving
-1 + t = -2.449489743

Solving for variable 't'.

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

Add '1' to each side of the equation.
-1 + 1 + t = -2.449489743 + 1

Combine like terms: -1 + 1 = 0
0 + t = -2.449489743 + 1
t = -2.449489743 + 1

Combine like terms: -2.449489743 + 1 = -1.449489743
t = -1.449489743

Simplifying
t = -1.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.449489743, -1.449489743}
Solution
t = {3.449489743, -1.449489743}