10(t-5)8t=6(3t+2)-8

Solution for 10(t-5)8t=6(3t+2)-8 equation:

Simplifying
10(t + -5) * 8t = 6(3t + 2) + -8

Reorder the terms:
10(-5 + t) * 8t = 6(3t + 2) + -8

Reorder the terms for easier multiplication:
10 * 8t(-5 + t) = 6(3t + 2) + -8

Multiply 10 * 8
80t(-5 + t) = 6(3t + 2) + -8
(-5 * 80t + t * 80t) = 6(3t + 2) + -8
(-400t + 80t2) = 6(3t + 2) + -8

Reorder the terms:
-400t + 80t2 = 6(2 + 3t) + -8
-400t + 80t2 = (2 * 6 + 3t * 6) + -8
-400t + 80t2 = (12 + 18t) + -8

Reorder the terms:
-400t + 80t2 = 12 + -8 + 18t

Combine like terms: 12 + -8 = 4
-400t + 80t2 = 4 + 18t

Solving
-400t + 80t2 = 4 + 18t

Solving for variable 't'.

Reorder the terms:
-4 + -400t + -18t + 80t2 = 4 + 18t + -4 + -18t

Combine like terms: -400t + -18t = -418t
-4 + -418t + 80t2 = 4 + 18t + -4 + -18t

Reorder the terms:
-4 + -418t + 80t2 = 4 + -4 + 18t + -18t

Combine like terms: 4 + -4 = 0
-4 + -418t + 80t2 = 0 + 18t + -18t
-4 + -418t + 80t2 = 18t + -18t

Combine like terms: 18t + -18t = 0
-4 + -418t + 80t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -209t + 40t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -209t + 40t2)' equal to zero and attempt to solve:

Simplifying
-2 + -209t + 40t2 = 0

Solving
-2 + -209t + 40t2 = 0

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

Divide each side by '40'.
-0.05 + -5.225t + t2 = 0.0

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -5.225t + 0.05 + t2 = 0.0 + 0.05

Reorder the terms:
-0.05 + 0.05 + -5.225t + t2 = 0.0 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -5.225t + t2 = 0.0 + 0.05
-5.225t + t2 = 0.0 + 0.05

Combine like terms: 0.0 + 0.05 = 0.05
-5.225t + t2 = 0.05

The t term is -5.225t.  Take half its coefficient (-2.6125).
Square it (6.82515625) and add it to both sides.

Add '6.82515625' to each side of the equation.
-5.225t + 6.82515625 + t2 = 0.05 + 6.82515625

Reorder the terms:
6.82515625 + -5.225t + t2 = 0.05 + 6.82515625

Combine like terms: 0.05 + 6.82515625 = 6.87515625
6.82515625 + -5.225t + t2 = 6.87515625

Factor a perfect square on the left side:
(t + -2.6125)(t + -2.6125) = 6.87515625

Calculate the square root of the right side: 2.622051916

Break this problem into two subproblems by setting 
(t + -2.6125) equal to 2.622051916 and -2.622051916.

Subproblem 1
t + -2.6125 = 2.622051916

Simplifying
t + -2.6125 = 2.622051916

Reorder the terms:
-2.6125 + t = 2.622051916

Solving
-2.6125 + t = 2.622051916

Solving for variable 't'.

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

Add '2.6125' to each side of the equation.
-2.6125 + 2.6125 + t = 2.622051916 + 2.6125

Combine like terms: -2.6125 + 2.6125 = 0.0000
0.0000 + t = 2.622051916 + 2.6125
t = 2.622051916 + 2.6125

Combine like terms: 2.622051916 + 2.6125 = 5.234551916
t = 5.234551916

Simplifying
t = 5.234551916

Subproblem 2
t + -2.6125 = -2.622051916

Simplifying
t + -2.6125 = -2.622051916

Reorder the terms:
-2.6125 + t = -2.622051916

Solving
-2.6125 + t = -2.622051916

Solving for variable 't'.

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

Add '2.6125' to each side of the equation.
-2.6125 + 2.6125 + t = -2.622051916 + 2.6125

Combine like terms: -2.6125 + 2.6125 = 0.0000
0.0000 + t = -2.622051916 + 2.6125
t = -2.622051916 + 2.6125

Combine like terms: -2.622051916 + 2.6125 = -0.009551916
t = -0.009551916

Simplifying
t = -0.009551916

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {5.234551916, -0.009551916}
Solution
t = {5.234551916, -0.009551916}