8(2t^2-13t-56)=0

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Solution for 8(2t^2-13t-56)=0 equation:


Simplifying
8(2t2 + -13t + -56) = 0

Reorder the terms:
8(-56 + -13t + 2t2) = 0
(-56 * 8 + -13t * 8 + 2t2 * 8) = 0
(-448 + -104t + 16t2) = 0

Solving
-448 + -104t + 16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-56 + -13t + 2t2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-56 + -13t + 2t2)' equal to zero and attempt to solve:

Simplifying
-56 + -13t + 2t2 = 0

Solving
-56 + -13t + 2t2 = 0

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

Divide each side by '2'.
-28 + -6.5t + t2 = 0

Move the constant term to the right:

Add '28' to each side of the equation.
-28 + -6.5t + 28 + t2 = 0 + 28

Reorder the terms:
-28 + 28 + -6.5t + t2 = 0 + 28

Combine like terms: -28 + 28 = 0
0 + -6.5t + t2 = 0 + 28
-6.5t + t2 = 0 + 28

Combine like terms: 0 + 28 = 28
-6.5t + t2 = 28

The t term is -6.5t.  Take half its coefficient (-3.25).
Square it (10.5625) and add it to both sides.

Add '10.5625' to each side of the equation.
-6.5t + 10.5625 + t2 = 28 + 10.5625

Reorder the terms:
10.5625 + -6.5t + t2 = 28 + 10.5625

Combine like terms: 28 + 10.5625 = 38.5625
10.5625 + -6.5t + t2 = 38.5625

Factor a perfect square on the left side:
(t + -3.25)(t + -3.25) = 38.5625

Calculate the square root of the right side: 6.209871174

Break this problem into two subproblems by setting 
(t + -3.25) equal to 6.209871174 and -6.209871174.


Subproblem 1
t + -3.25 = 6.209871174

Simplifying
t + -3.25 = 6.209871174

Reorder the terms:
-3.25 + t = 6.209871174

Solving
-3.25 + t = 6.209871174

Solving for variable 't'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + t = 6.209871174 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + t = 6.209871174 + 3.25
t = 6.209871174 + 3.25

Combine like terms: 6.209871174 + 3.25 = 9.459871174
t = 9.459871174

Simplifying
t = 9.459871174


Subproblem 2
t + -3.25 = -6.209871174

Simplifying
t + -3.25 = -6.209871174

Reorder the terms:
-3.25 + t = -6.209871174

Solving
-3.25 + t = -6.209871174

Solving for variable 't'.

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

Add '3.25' to each side of the equation.
-3.25 + 3.25 + t = -6.209871174 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + t = -6.209871174 + 3.25
t = -6.209871174 + 3.25

Combine like terms: -6.209871174 + 3.25 = -2.959871174
t = -2.959871174

Simplifying
t = -2.959871174


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {9.459871174, -2.959871174}
Solution
t = {9.459871174, -2.959871174}

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