-2t(5t-2)+8t=7t-3

Solution for -2t(5t-2)+8t=7t-3 equation:

Simplifying
-2t(5t + -2) + 8t = 7t + -3

Reorder the terms:
-2t(-2 + 5t) + 8t = 7t + -3
(-2 * -2t + 5t * -2t) + 8t = 7t + -3
(4t + -10t2) + 8t = 7t + -3

Reorder the terms:
4t + 8t + -10t2 = 7t + -3

Combine like terms: 4t + 8t = 12t
12t + -10t2 = 7t + -3

Reorder the terms:
12t + -10t2 = -3 + 7t

Solving
12t + -10t2 = -3 + 7t

Solving for variable 't'.

Reorder the terms:
3 + 12t + -7t + -10t2 = -3 + 7t + 3 + -7t

Combine like terms: 12t + -7t = 5t
3 + 5t + -10t2 = -3 + 7t + 3 + -7t

Reorder the terms:
3 + 5t + -10t2 = -3 + 3 + 7t + -7t

Combine like terms: -3 + 3 = 0
3 + 5t + -10t2 = 0 + 7t + -7t
3 + 5t + -10t2 = 7t + -7t

Combine like terms: 7t + -7t = 0
3 + 5t + -10t2 = 0

Begin completing the square.  Divide all terms by
-10 the coefficient of the squared term: 

Divide each side by '-10'.
-0.3 + -0.5t + t2 = 0.0

Move the constant term to the right:

Add '0.3' to each side of the equation.
-0.3 + -0.5t + 0.3 + t2 = 0.0 + 0.3

Reorder the terms:
-0.3 + 0.3 + -0.5t + t2 = 0.0 + 0.3

Combine like terms: -0.3 + 0.3 = 0.0
0.0 + -0.5t + t2 = 0.0 + 0.3
-0.5t + t2 = 0.0 + 0.3

Combine like terms: 0.0 + 0.3 = 0.3
-0.5t + t2 = 0.3

The t term is -0.5t.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5t + 0.0625 + t2 = 0.3 + 0.0625

Reorder the terms:
0.0625 + -0.5t + t2 = 0.3 + 0.0625

Combine like terms: 0.3 + 0.0625 = 0.3625
0.0625 + -0.5t + t2 = 0.3625

Factor a perfect square on the left side:
(t + -0.25)(t + -0.25) = 0.3625

Calculate the square root of the right side: 0.602079729

Break this problem into two subproblems by setting 
(t + -0.25) equal to 0.602079729 and -0.602079729.

Subproblem 1
t + -0.25 = 0.602079729

Simplifying
t + -0.25 = 0.602079729

Reorder the terms:
-0.25 + t = 0.602079729

Solving
-0.25 + t = 0.602079729

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = 0.602079729 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = 0.602079729 + 0.25
t = 0.602079729 + 0.25

Combine like terms: 0.602079729 + 0.25 = 0.852079729
t = 0.852079729

Simplifying
t = 0.852079729

Subproblem 2
t + -0.25 = -0.602079729

Simplifying
t + -0.25 = -0.602079729

Reorder the terms:
-0.25 + t = -0.602079729

Solving
-0.25 + t = -0.602079729

Solving for variable 't'.

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

Add '0.25' to each side of the equation.
-0.25 + 0.25 + t = -0.602079729 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + t = -0.602079729 + 0.25
t = -0.602079729 + 0.25

Combine like terms: -0.602079729 + 0.25 = -0.352079729
t = -0.352079729

Simplifying
t = -0.352079729

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.852079729, -0.352079729}