-2(t+2)*5t=6t+11

Solution for -2(t+2)*5t=6t+11 equation:

Simplifying
-2(t + 2) * 5t = 6t + 11

Reorder the terms:
-2(2 + t) * 5t = 6t + 11

Reorder the terms for easier multiplication:
-2 * 5t(2 + t) = 6t + 11

Multiply -2 * 5
-10t(2 + t) = 6t + 11
(2 * -10t + t * -10t) = 6t + 11
(-20t + -10t2) = 6t + 11

Reorder the terms:
-20t + -10t2 = 11 + 6t

Solving
-20t + -10t2 = 11 + 6t

Solving for variable 't'.

Reorder the terms:
-11 + -20t + -6t + -10t2 = 11 + 6t + -11 + -6t

Combine like terms: -20t + -6t = -26t
-11 + -26t + -10t2 = 11 + 6t + -11 + -6t

Reorder the terms:
-11 + -26t + -10t2 = 11 + -11 + 6t + -6t

Combine like terms: 11 + -11 = 0
-11 + -26t + -10t2 = 0 + 6t + -6t
-11 + -26t + -10t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
-11 + -26t + -10t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(11 + 26t + 10t2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(11 + 26t + 10t2)' equal to zero and attempt to solve:

Simplifying
11 + 26t + 10t2 = 0

Solving
11 + 26t + 10t2 = 0

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

Divide each side by '10'.
1.1 + 2.6t + t2 = 0.0

Move the constant term to the right:

Add '-1.1' to each side of the equation.
1.1 + 2.6t + -1.1 + t2 = 0.0 + -1.1

Reorder the terms:
1.1 + -1.1 + 2.6t + t2 = 0.0 + -1.1

Combine like terms: 1.1 + -1.1 = 0.0
0.0 + 2.6t + t2 = 0.0 + -1.1
2.6t + t2 = 0.0 + -1.1

Combine like terms: 0.0 + -1.1 = -1.1
2.6t + t2 = -1.1

The t term is 2.6t.  Take half its coefficient (1.3).
Square it (1.69) and add it to both sides.

Add '1.69' to each side of the equation.
2.6t + 1.69 + t2 = -1.1 + 1.69

Reorder the terms:
1.69 + 2.6t + t2 = -1.1 + 1.69

Combine like terms: -1.1 + 1.69 = 0.59
1.69 + 2.6t + t2 = 0.59

Factor a perfect square on the left side:
(t + 1.3)(t + 1.3) = 0.59

Calculate the square root of the right side: 0.768114575

Break this problem into two subproblems by setting 
(t + 1.3) equal to 0.768114575 and -0.768114575.

Subproblem 1
t + 1.3 = 0.768114575

Simplifying
t + 1.3 = 0.768114575

Reorder the terms:
1.3 + t = 0.768114575

Solving
1.3 + t = 0.768114575

Solving for variable 't'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + t = 0.768114575 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = 0.768114575 + -1.3
t = 0.768114575 + -1.3

Combine like terms: 0.768114575 + -1.3 = -0.531885425
t = -0.531885425

Simplifying
t = -0.531885425

Subproblem 2
t + 1.3 = -0.768114575

Simplifying
t + 1.3 = -0.768114575

Reorder the terms:
1.3 + t = -0.768114575

Solving
1.3 + t = -0.768114575

Solving for variable 't'.

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

Add '-1.3' to each side of the equation.
1.3 + -1.3 + t = -0.768114575 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = -0.768114575 + -1.3
t = -0.768114575 + -1.3

Combine like terms: -0.768114575 + -1.3 = -2.068114575
t = -2.068114575

Simplifying
t = -2.068114575

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.531885425, -2.068114575}
Solution
t = {-0.531885425, -2.068114575}