(10t^2+1t-6)=0

Solution for (10t^2+1t-6)=0 equation:

Simplifying
(10t2 + 1t + -6) = 0

Reorder the terms:
(-6 + 1t + 10t2) = 0

Remove parenthesis around (-6 + 1t + 10t2)
-6 + 1t + 10t2 = 0

Solving
-6 + 1t + 10t2 = 0

Solving for variable 't'.

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

Divide each side by '10'.
-0.6 + 0.1t + t2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + 0.1t + 0.6 + t2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + 0.1t + t2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + 0.1t + t2 = 0 + 0.6
0.1t + t2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
0.1t + t2 = 0.6

The t term is 0.1t.  Take half its coefficient (0.05).
Square it (0.0025) and add it to both sides.

Add '0.0025' to each side of the equation.
0.1t + 0.0025 + t2 = 0.6 + 0.0025

Reorder the terms:
0.0025 + 0.1t + t2 = 0.6 + 0.0025

Combine like terms: 0.6 + 0.0025 = 0.6025
0.0025 + 0.1t + t2 = 0.6025

Factor a perfect square on the left side:
(t + 0.05)(t + 0.05) = 0.6025

Calculate the square root of the right side: 0.776208735

Break this problem into two subproblems by setting 
(t + 0.05) equal to 0.776208735 and -0.776208735.

Subproblem 1
t + 0.05 = 0.776208735

Simplifying
t + 0.05 = 0.776208735

Reorder the terms:
0.05 + t = 0.776208735

Solving
0.05 + t = 0.776208735

Solving for variable 't'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + t = 0.776208735 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + t = 0.776208735 + -0.05
t = 0.776208735 + -0.05

Combine like terms: 0.776208735 + -0.05 = 0.726208735
t = 0.726208735

Simplifying
t = 0.726208735

Subproblem 2
t + 0.05 = -0.776208735

Simplifying
t + 0.05 = -0.776208735

Reorder the terms:
0.05 + t = -0.776208735

Solving
0.05 + t = -0.776208735

Solving for variable 't'.

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

Add '-0.05' to each side of the equation.
0.05 + -0.05 + t = -0.776208735 + -0.05

Combine like terms: 0.05 + -0.05 = 0.00
0.00 + t = -0.776208735 + -0.05
t = -0.776208735 + -0.05

Combine like terms: -0.776208735 + -0.05 = -0.826208735
t = -0.826208735

Simplifying
t = -0.826208735

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {0.726208735, -0.826208735}