t(2t+5)=5

Solution for t(2t+5)=5 equation:

Simplifying
t(2t + 5) = 5

Reorder the terms:
t(5 + 2t) = 5
(5 * t + 2t * t) = 5
(5t + 2t2) = 5

Solving
5t + 2t2 = 5

Solving for variable 't'.

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

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

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

Divide each side by '2'.
-2.5 + 2.5t + t2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2.5t + 2.5 + t2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2.5t + t2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2.5t + t2 = 0 + 2.5
2.5t + t2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2.5t + t2 = 2.5

The t term is 2.5t.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5t + 1.5625 + t2 = 2.5 + 1.5625

Reorder the terms:
1.5625 + 2.5t + t2 = 2.5 + 1.5625

Combine like terms: 2.5 + 1.5625 = 4.0625
1.5625 + 2.5t + t2 = 4.0625

Factor a perfect square on the left side:
(t + 1.25)(t + 1.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(t + 1.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
t + 1.25 = 2.015564437

Simplifying
t + 1.25 = 2.015564437

Reorder the terms:
1.25 + t = 2.015564437

Solving
1.25 + t = 2.015564437

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = 2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = 2.015564437 + -1.25
t = 2.015564437 + -1.25

Combine like terms: 2.015564437 + -1.25 = 0.765564437
t = 0.765564437

Simplifying
t = 0.765564437

Subproblem 2
t + 1.25 = -2.015564437

Simplifying
t + 1.25 = -2.015564437

Reorder the terms:
1.25 + t = -2.015564437

Solving
1.25 + t = -2.015564437

Solving for variable 't'.

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

Add '-1.25' to each side of the equation.
1.25 + -1.25 + t = -2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + t = -2.015564437 + -1.25
t = -2.015564437 + -1.25

Combine like terms: -2.015564437 + -1.25 = -3.265564437
t = -3.265564437

Simplifying
t = -3.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.765564437, -3.265564437}