-5t(t-1)+8t=7t-2

Solution for -5t(t-1)+8t=7t-2 equation:

Simplifying
-5t(t + -1) + 8t = 7t + -2

Reorder the terms:
-5t(-1 + t) + 8t = 7t + -2
(-1 * -5t + t * -5t) + 8t = 7t + -2
(5t + -5t2) + 8t = 7t + -2

Reorder the terms:
5t + 8t + -5t2 = 7t + -2

Combine like terms: 5t + 8t = 13t
13t + -5t2 = 7t + -2

Reorder the terms:
13t + -5t2 = -2 + 7t

Solving
13t + -5t2 = -2 + 7t

Solving for variable 't'.

Reorder the terms:
2 + 13t + -7t + -5t2 = -2 + 7t + 2 + -7t

Combine like terms: 13t + -7t = 6t
2 + 6t + -5t2 = -2 + 7t + 2 + -7t

Reorder the terms:
2 + 6t + -5t2 = -2 + 2 + 7t + -7t

Combine like terms: -2 + 2 = 0
2 + 6t + -5t2 = 0 + 7t + -7t
2 + 6t + -5t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
2 + 6t + -5t2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.4 + -1.2t + t2 = 0

Move the constant term to the right:

Add '0.4' to each side of the equation.
-0.4 + -1.2t + 0.4 + t2 = 0 + 0.4

Reorder the terms:
-0.4 + 0.4 + -1.2t + t2 = 0 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + -1.2t + t2 = 0 + 0.4
-1.2t + t2 = 0 + 0.4

Combine like terms: 0 + 0.4 = 0.4
-1.2t + t2 = 0.4

The t term is -1.2t.  Take half its coefficient (-0.6).
Square it (0.36) and add it to both sides.

Add '0.36' to each side of the equation.
-1.2t + 0.36 + t2 = 0.4 + 0.36

Reorder the terms:
0.36 + -1.2t + t2 = 0.4 + 0.36

Combine like terms: 0.4 + 0.36 = 0.76
0.36 + -1.2t + t2 = 0.76

Factor a perfect square on the left side:
(t + -0.6)(t + -0.6) = 0.76

Calculate the square root of the right side: 0.871779789

Break this problem into two subproblems by setting 
(t + -0.6) equal to 0.871779789 and -0.871779789.

Subproblem 1
t + -0.6 = 0.871779789

Simplifying
t + -0.6 = 0.871779789

Reorder the terms:
-0.6 + t = 0.871779789

Solving
-0.6 + t = 0.871779789

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = 0.871779789 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = 0.871779789 + 0.6
t = 0.871779789 + 0.6

Combine like terms: 0.871779789 + 0.6 = 1.471779789
t = 1.471779789

Simplifying
t = 1.471779789

Subproblem 2
t + -0.6 = -0.871779789

Simplifying
t + -0.6 = -0.871779789

Reorder the terms:
-0.6 + t = -0.871779789

Solving
-0.6 + t = -0.871779789

Solving for variable 't'.

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

Add '0.6' to each side of the equation.
-0.6 + 0.6 + t = -0.871779789 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + t = -0.871779789 + 0.6
t = -0.871779789 + 0.6

Combine like terms: -0.871779789 + 0.6 = -0.271779789
t = -0.271779789

Simplifying
t = -0.271779789

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.471779789, -0.271779789}