-5(t-5)57t=8t-6

Solution for -5(t-5)57t=8t-6 equation:

Simplifying
-5(t + -5) * 57t = 8t + -6

Reorder the terms:
-5(-5 + t) * 57t = 8t + -6

Reorder the terms for easier multiplication:
-5 * 57t(-5 + t) = 8t + -6

Multiply -5 * 57
-285t(-5 + t) = 8t + -6
(-5 * -285t + t * -285t) = 8t + -6
(1425t + -285t2) = 8t + -6

Reorder the terms:
1425t + -285t2 = -6 + 8t

Solving
1425t + -285t2 = -6 + 8t

Solving for variable 't'.

Reorder the terms:
6 + 1425t + -8t + -285t2 = -6 + 8t + 6 + -8t

Combine like terms: 1425t + -8t = 1417t
6 + 1417t + -285t2 = -6 + 8t + 6 + -8t

Reorder the terms:
6 + 1417t + -285t2 = -6 + 6 + 8t + -8t

Combine like terms: -6 + 6 = 0
6 + 1417t + -285t2 = 0 + 8t + -8t
6 + 1417t + -285t2 = 8t + -8t

Combine like terms: 8t + -8t = 0
6 + 1417t + -285t2 = 0

Begin completing the square.  Divide all terms by
-285 the coefficient of the squared term: 

Divide each side by '-285'.
-0.02105263158 + -4.971929825t + t2 = 0

Move the constant term to the right:

Add '0.02105263158' to each side of the equation.
-0.02105263158 + -4.971929825t + 0.02105263158 + t2 = 0 + 0.02105263158

Reorder the terms:
-0.02105263158 + 0.02105263158 + -4.971929825t + t2 = 0 + 0.02105263158

Combine like terms: -0.02105263158 + 0.02105263158 = 0.00000000000
0.00000000000 + -4.971929825t + t2 = 0 + 0.02105263158
-4.971929825t + t2 = 0 + 0.02105263158

Combine like terms: 0 + 0.02105263158 = 0.02105263158
-4.971929825t + t2 = 0.02105263158

The t term is -4.971929825t.  Take half its coefficient (-2.485964913).
Square it (6.180021549) and add it to both sides.

Add '6.180021549' to each side of the equation.
-4.971929825t + 6.180021549 + t2 = 0.02105263158 + 6.180021549

Reorder the terms:
6.180021549 + -4.971929825t + t2 = 0.02105263158 + 6.180021549

Combine like terms: 0.02105263158 + 6.180021549 = 6.20107418058
6.180021549 + -4.971929825t + t2 = 6.20107418058

Factor a perfect square on the left side:
(t + -2.485964913)(t + -2.485964913) = 6.20107418058

Calculate the square root of the right side: 2.490195611

Break this problem into two subproblems by setting 
(t + -2.485964913) equal to 2.490195611 and -2.490195611.

Subproblem 1
t + -2.485964913 = 2.490195611

Simplifying
t + -2.485964913 = 2.490195611

Reorder the terms:
-2.485964913 + t = 2.490195611

Solving
-2.485964913 + t = 2.490195611

Solving for variable 't'.

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

Add '2.485964913' to each side of the equation.
-2.485964913 + 2.485964913 + t = 2.490195611 + 2.485964913

Combine like terms: -2.485964913 + 2.485964913 = 0.000000000
0.000000000 + t = 2.490195611 + 2.485964913
t = 2.490195611 + 2.485964913

Combine like terms: 2.490195611 + 2.485964913 = 4.976160524
t = 4.976160524

Simplifying
t = 4.976160524

Subproblem 2
t + -2.485964913 = -2.490195611

Simplifying
t + -2.485964913 = -2.490195611

Reorder the terms:
-2.485964913 + t = -2.490195611

Solving
-2.485964913 + t = -2.490195611

Solving for variable 't'.

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

Add '2.485964913' to each side of the equation.
-2.485964913 + 2.485964913 + t = -2.490195611 + 2.485964913

Combine like terms: -2.485964913 + 2.485964913 = 0.000000000
0.000000000 + t = -2.490195611 + 2.485964913
t = -2.490195611 + 2.485964913

Combine like terms: -2.490195611 + 2.485964913 = -0.004230698
t = -0.004230698

Simplifying
t = -0.004230698

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {4.976160524, -0.004230698}