20+4t=5t(t+4)

Solution for 20+4t=5t(t+4) equation:

Simplifying
20 + 4t = 5t(t + 4)

Reorder the terms:
20 + 4t = 5t(4 + t)
20 + 4t = (4 * 5t + t * 5t)
20 + 4t = (20t + 5t2)

Solving
20 + 4t = 20t + 5t2

Solving for variable 't'.

Combine like terms: 4t + -20t = -16t
20 + -16t + -5t2 = 20t + 5t2 + -20t + -5t2

Reorder the terms:
20 + -16t + -5t2 = 20t + -20t + 5t2 + -5t2

Combine like terms: 20t + -20t = 0
20 + -16t + -5t2 = 0 + 5t2 + -5t2
20 + -16t + -5t2 = 5t2 + -5t2

Combine like terms: 5t2 + -5t2 = 0
20 + -16t + -5t2 = 0

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

Divide each side by '-5'.
-4 + 3.2t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + 3.2t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + 3.2t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + 3.2t + t2 = 0 + 4
3.2t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
3.2t + t2 = 4

The t term is 3.2t.  Take half its coefficient (1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
3.2t + 2.56 + t2 = 4 + 2.56

Reorder the terms:
2.56 + 3.2t + t2 = 4 + 2.56

Combine like terms: 4 + 2.56 = 6.56
2.56 + 3.2t + t2 = 6.56

Factor a perfect square on the left side:
(t + 1.6)(t + 1.6) = 6.56

Calculate the square root of the right side: 2.561249695

Break this problem into two subproblems by setting 
(t + 1.6) equal to 2.561249695 and -2.561249695.

Subproblem 1
t + 1.6 = 2.561249695

Simplifying
t + 1.6 = 2.561249695

Reorder the terms:
1.6 + t = 2.561249695

Solving
1.6 + t = 2.561249695

Solving for variable 't'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + t = 2.561249695 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + t = 2.561249695 + -1.6
t = 2.561249695 + -1.6

Combine like terms: 2.561249695 + -1.6 = 0.961249695
t = 0.961249695

Simplifying
t = 0.961249695

Subproblem 2
t + 1.6 = -2.561249695

Simplifying
t + 1.6 = -2.561249695

Reorder the terms:
1.6 + t = -2.561249695

Solving
1.6 + t = -2.561249695

Solving for variable 't'.

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

Add '-1.6' to each side of the equation.
1.6 + -1.6 + t = -2.561249695 + -1.6

Combine like terms: 1.6 + -1.6 = 0.0
0.0 + t = -2.561249695 + -1.6
t = -2.561249695 + -1.6

Combine like terms: -2.561249695 + -1.6 = -4.161249695
t = -4.161249695

Simplifying
t = -4.161249695

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.961249695, -4.161249695}