79(t+50)+79t=t(t+50)

Solution for 79(t+50)+79t=t(t+50) equation:

Simplifying
79(t + 50) + 79t = t(t + 50)

Reorder the terms:
79(50 + t) + 79t = t(t + 50)
(50 * 79 + t * 79) + 79t = t(t + 50)
(3950 + 79t) + 79t = t(t + 50)

Combine like terms: 79t + 79t = 158t
3950 + 158t = t(t + 50)

Reorder the terms:
3950 + 158t = t(50 + t)
3950 + 158t = (50 * t + t * t)
3950 + 158t = (50t + t2)

Solving
3950 + 158t = 50t + t2

Solving for variable 't'.

Combine like terms: 158t + -50t = 108t
3950 + 108t + -1t2 = 50t + t2 + -50t + -1t2

Reorder the terms:
3950 + 108t + -1t2 = 50t + -50t + t2 + -1t2

Combine like terms: 50t + -50t = 0
3950 + 108t + -1t2 = 0 + t2 + -1t2
3950 + 108t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
3950 + 108t + -1t2 = 0

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

Divide each side by '-1'.
-3950 + -108t + t2 = 0

Move the constant term to the right:

Add '3950' to each side of the equation.
-3950 + -108t + 3950 + t2 = 0 + 3950

Reorder the terms:
-3950 + 3950 + -108t + t2 = 0 + 3950

Combine like terms: -3950 + 3950 = 0
0 + -108t + t2 = 0 + 3950
-108t + t2 = 0 + 3950

Combine like terms: 0 + 3950 = 3950
-108t + t2 = 3950

The t term is -108t.  Take half its coefficient (-54).
Square it (2916) and add it to both sides.

Add '2916' to each side of the equation.
-108t + 2916 + t2 = 3950 + 2916

Reorder the terms:
2916 + -108t + t2 = 3950 + 2916

Combine like terms: 3950 + 2916 = 6866
2916 + -108t + t2 = 6866

Factor a perfect square on the left side:
(t + -54)(t + -54) = 6866

Calculate the square root of the right side: 82.861329943

Break this problem into two subproblems by setting 
(t + -54) equal to 82.861329943 and -82.861329943.

Subproblem 1
t + -54 = 82.861329943

Simplifying
t + -54 = 82.861329943

Reorder the terms:
-54 + t = 82.861329943

Solving
-54 + t = 82.861329943

Solving for variable 't'.

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

Add '54' to each side of the equation.
-54 + 54 + t = 82.861329943 + 54

Combine like terms: -54 + 54 = 0
0 + t = 82.861329943 + 54
t = 82.861329943 + 54

Combine like terms: 82.861329943 + 54 = 136.861329943
t = 136.861329943

Simplifying
t = 136.861329943

Subproblem 2
t + -54 = -82.861329943

Simplifying
t + -54 = -82.861329943

Reorder the terms:
-54 + t = -82.861329943

Solving
-54 + t = -82.861329943

Solving for variable 't'.

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

Add '54' to each side of the equation.
-54 + 54 + t = -82.861329943 + 54

Combine like terms: -54 + 54 = 0
0 + t = -82.861329943 + 54
t = -82.861329943 + 54

Combine like terms: -82.861329943 + 54 = -28.861329943
t = -28.861329943

Simplifying
t = -28.861329943

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {136.861329943, -28.861329943}