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

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

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

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

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

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

Reorder the terms:
-20t + -10t2 = 2 + 6t

Solving
-20t + -10t2 = 2 + 6t

Solving for variable 't'.

Reorder the terms:
-2 + -20t + -6t + -10t2 = 2 + 6t + -2 + -6t

Combine like terms: -20t + -6t = -26t
-2 + -26t + -10t2 = 2 + 6t + -2 + -6t

Reorder the terms:
-2 + -26t + -10t2 = 2 + -2 + 6t + -6t

Combine like terms: 2 + -2 = 0
-2 + -26t + -10t2 = 0 + 6t + -6t
-2 + -26t + -10t2 = 6t + -6t

Combine like terms: 6t + -6t = 0
-2 + -26t + -10t2 = 0

Factor out the Greatest Common Factor (GCF), '-2'.
-2(1 + 13t + 5t2) = 0

Ignore the factor -2.
Subproblem 1
Set the factor '(1 + 13t + 5t2)' equal to zero and attempt to solve:

Simplifying
1 + 13t + 5t2 = 0

Solving
1 + 13t + 5t2 = 0

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

Divide each side by '5'.
0.2 + 2.6t + t2 = 0

Move the constant term to the right:

Add '-0.2' to each side of the equation.
0.2 + 2.6t + -0.2 + t2 = 0 + -0.2

Reorder the terms:
0.2 + -0.2 + 2.6t + t2 = 0 + -0.2

Combine like terms: 0.2 + -0.2 = 0.0
0.0 + 2.6t + t2 = 0 + -0.2
2.6t + t2 = 0 + -0.2

Combine like terms: 0 + -0.2 = -0.2
2.6t + t2 = -0.2

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 = -0.2 + 1.69

Reorder the terms:
1.69 + 2.6t + t2 = -0.2 + 1.69

Combine like terms: -0.2 + 1.69 = 1.49
1.69 + 2.6t + t2 = 1.49

Factor a perfect square on the left side:
(t + 1.3)(t + 1.3) = 1.49

Calculate the square root of the right side: 1.220655562

Break this problem into two subproblems by setting 
(t + 1.3) equal to 1.220655562 and -1.220655562.

Subproblem 1
t + 1.3 = 1.220655562

Simplifying
t + 1.3 = 1.220655562

Reorder the terms:
1.3 + t = 1.220655562

Solving
1.3 + t = 1.220655562

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 = 1.220655562 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = 1.220655562 + -1.3
t = 1.220655562 + -1.3

Combine like terms: 1.220655562 + -1.3 = -0.079344438
t = -0.079344438

Simplifying
t = -0.079344438

Subproblem 2
t + 1.3 = -1.220655562

Simplifying
t + 1.3 = -1.220655562

Reorder the terms:
1.3 + t = -1.220655562

Solving
1.3 + t = -1.220655562

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 = -1.220655562 + -1.3

Combine like terms: 1.3 + -1.3 = 0.0
0.0 + t = -1.220655562 + -1.3
t = -1.220655562 + -1.3

Combine like terms: -1.220655562 + -1.3 = -2.520655562
t = -2.520655562

Simplifying
t = -2.520655562

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {-0.079344438, -2.520655562}
Solution
t = {-0.079344438, -2.520655562}