10+4t=t(t+2)

Solution for 10+4t=t(t+2) equation:

Simplifying
10 + 4t = t(t + 2)

Reorder the terms:
10 + 4t = t(2 + t)
10 + 4t = (2 * t + t * t)
10 + 4t = (2t + t2)

Solving
10 + 4t = 2t + t2

Solving for variable 't'.

Combine like terms: 4t + -2t = 2t
10 + 2t + -1t2 = 2t + t2 + -2t + -1t2

Reorder the terms:
10 + 2t + -1t2 = 2t + -2t + t2 + -1t2

Combine like terms: 2t + -2t = 0
10 + 2t + -1t2 = 0 + t2 + -1t2
10 + 2t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
10 + 2t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-10 + -2t + t2 = 0

Move the constant term to the right:

Add '10' to each side of the equation.
-10 + -2t + 10 + t2 = 0 + 10

Reorder the terms:
-10 + 10 + -2t + t2 = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -2t + t2 = 0 + 10
-2t + t2 = 0 + 10

Combine like terms: 0 + 10 = 10
-2t + t2 = 10

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 = 10 + 1

Reorder the terms:
1 + -2t + t2 = 10 + 1

Combine like terms: 10 + 1 = 11
1 + -2t + t2 = 11

Factor a perfect square on the left side:
(t + -1)(t + -1) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(t + -1) equal to 3.31662479 and -3.31662479.

Subproblem 1
t + -1 = 3.31662479

Simplifying
t + -1 = 3.31662479

Reorder the terms:
-1 + t = 3.31662479

Solving
-1 + t = 3.31662479

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 = 3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + t = 3.31662479 + 1
t = 3.31662479 + 1

Combine like terms: 3.31662479 + 1 = 4.31662479
t = 4.31662479

Simplifying
t = 4.31662479

Subproblem 2
t + -1 = -3.31662479

Simplifying
t + -1 = -3.31662479

Reorder the terms:
-1 + t = -3.31662479

Solving
-1 + t = -3.31662479

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 = -3.31662479 + 1

Combine like terms: -1 + 1 = 0
0 + t = -3.31662479 + 1
t = -3.31662479 + 1

Combine like terms: -3.31662479 + 1 = -2.31662479
t = -2.31662479

Simplifying
t = -2.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.31662479, -2.31662479}