(t+4)*2t=67

Solution for (t+4)*2t=67 equation:

Simplifying
(t + 4) * 2t = 67

Reorder the terms:
(4 + t) * 2t = 67

Reorder the terms for easier multiplication:
2t(4 + t) = 67
(4 * 2t + t * 2t) = 67
(8t + 2t2) = 67

Solving
8t + 2t2 = 67

Solving for variable 't'.

Reorder the terms:
-67 + 8t + 2t2 = 67 + -67

Combine like terms: 67 + -67 = 0
-67 + 8t + 2t2 = 0

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

Divide each side by '2'.
-33.5 + 4t + t2 = 0

Move the constant term to the right:

Add '33.5' to each side of the equation.
-33.5 + 4t + 33.5 + t2 = 0 + 33.5

Reorder the terms:
-33.5 + 33.5 + 4t + t2 = 0 + 33.5

Combine like terms: -33.5 + 33.5 = 0.0
0.0 + 4t + t2 = 0 + 33.5
4t + t2 = 0 + 33.5

Combine like terms: 0 + 33.5 = 33.5
4t + t2 = 33.5

The t term is 4t.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4t + 4 + t2 = 33.5 + 4

Reorder the terms:
4 + 4t + t2 = 33.5 + 4

Combine like terms: 33.5 + 4 = 37.5
4 + 4t + t2 = 37.5

Factor a perfect square on the left side:
(t + 2)(t + 2) = 37.5

Calculate the square root of the right side: 6.123724357

Break this problem into two subproblems by setting 
(t + 2) equal to 6.123724357 and -6.123724357.

Subproblem 1
t + 2 = 6.123724357

Simplifying
t + 2 = 6.123724357

Reorder the terms:
2 + t = 6.123724357

Solving
2 + t = 6.123724357

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = 6.123724357 + -2

Combine like terms: 2 + -2 = 0
0 + t = 6.123724357 + -2
t = 6.123724357 + -2

Combine like terms: 6.123724357 + -2 = 4.123724357
t = 4.123724357

Simplifying
t = 4.123724357

Subproblem 2
t + 2 = -6.123724357

Simplifying
t + 2 = -6.123724357

Reorder the terms:
2 + t = -6.123724357

Solving
2 + t = -6.123724357

Solving for variable 't'.

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

Add '-2' to each side of the equation.
2 + -2 + t = -6.123724357 + -2

Combine like terms: 2 + -2 = 0
0 + t = -6.123724357 + -2
t = -6.123724357 + -2

Combine like terms: -6.123724357 + -2 = -8.123724357
t = -8.123724357

Simplifying
t = -8.123724357

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.123724357, -8.123724357}