(5t+1)25t=5

Solution for (5t+1)25t=5 equation:

Simplifying
(5t + 1) * 25t = 5

Reorder the terms:
(1 + 5t) * 25t = 5

Reorder the terms for easier multiplication:
25t(1 + 5t) = 5
(1 * 25t + 5t * 25t) = 5
(25t + 125t2) = 5

Solving
25t + 125t2 = 5

Solving for variable 't'.

Reorder the terms:
-5 + 25t + 125t2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + 25t + 125t2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-1 + 5t + 25t2) = 0

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + 5t + 25t2)' equal to zero and attempt to solve:

Simplifying
-1 + 5t + 25t2 = 0

Solving
-1 + 5t + 25t2 = 0

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

Divide each side by '25'.
-0.04 + 0.2t + t2 = 0

Move the constant term to the right:

Add '0.04' to each side of the equation.
-0.04 + 0.2t + 0.04 + t2 = 0 + 0.04

Reorder the terms:
-0.04 + 0.04 + 0.2t + t2 = 0 + 0.04

Combine like terms: -0.04 + 0.04 = 0.00
0.00 + 0.2t + t2 = 0 + 0.04
0.2t + t2 = 0 + 0.04

Combine like terms: 0 + 0.04 = 0.04
0.2t + t2 = 0.04

The t term is 0.2t.  Take half its coefficient (0.1).
Square it (0.01) and add it to both sides.

Add '0.01' to each side of the equation.
0.2t + 0.01 + t2 = 0.04 + 0.01

Reorder the terms:
0.01 + 0.2t + t2 = 0.04 + 0.01

Combine like terms: 0.04 + 0.01 = 0.05
0.01 + 0.2t + t2 = 0.05

Factor a perfect square on the left side:
(t + 0.1)(t + 0.1) = 0.05

Calculate the square root of the right side: 0.223606798

Break this problem into two subproblems by setting 
(t + 0.1) equal to 0.223606798 and -0.223606798.

Subproblem 1
t + 0.1 = 0.223606798

Simplifying
t + 0.1 = 0.223606798

Reorder the terms:
0.1 + t = 0.223606798

Solving
0.1 + t = 0.223606798

Solving for variable 't'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + t = 0.223606798 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + t = 0.223606798 + -0.1
t = 0.223606798 + -0.1

Combine like terms: 0.223606798 + -0.1 = 0.123606798
t = 0.123606798

Simplifying
t = 0.123606798

Subproblem 2
t + 0.1 = -0.223606798

Simplifying
t + 0.1 = -0.223606798

Reorder the terms:
0.1 + t = -0.223606798

Solving
0.1 + t = -0.223606798

Solving for variable 't'.

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

Add '-0.1' to each side of the equation.
0.1 + -0.1 + t = -0.223606798 + -0.1

Combine like terms: 0.1 + -0.1 = 0.0
0.0 + t = -0.223606798 + -0.1
t = -0.223606798 + -0.1

Combine like terms: -0.223606798 + -0.1 = -0.323606798
t = -0.323606798

Simplifying
t = -0.323606798

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.123606798, -0.323606798}
Solution
t = {0.123606798, -0.323606798}