36=.3t^2+.6t

Solution for 36=.3t^2+.6t equation:

Simplifying
36 = 0.3t2 + 0.6t

Reorder the terms:
36 = 0.6t + 0.3t2

Solving
36 = 0.6t + 0.3t2

Solving for variable 't'.

Reorder the terms:
36 + -0.6t + -0.3t2 = 0.6t + -0.6t + 0.3t2 + -0.3t2

Combine like terms: 0.6t + -0.6t = 0.0
36 + -0.6t + -0.3t2 = 0.0 + 0.3t2 + -0.3t2
36 + -0.6t + -0.3t2 = 0.3t2 + -0.3t2

Combine like terms: 0.3t2 + -0.3t2 = 0.0
36 + -0.6t + -0.3t2 = 0.0

Begin completing the square.  Divide all terms by
-0.3 the coefficient of the squared term: 

Divide each side by '-0.3'.
-120 + 2t + t2 = 0

Move the constant term to the right:

Add '120' to each side of the equation.
-120 + 2t + 120 + t2 = 0 + 120

Reorder the terms:
-120 + 120 + 2t + t2 = 0 + 120

Combine like terms: -120 + 120 = 0
0 + 2t + t2 = 0 + 120
2t + t2 = 0 + 120

Combine like terms: 0 + 120 = 120
2t + t2 = 120

The t term is 2t.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2t + 1 + t2 = 120 + 1

Reorder the terms:
1 + 2t + t2 = 120 + 1

Combine like terms: 120 + 1 = 121
1 + 2t + t2 = 121

Factor a perfect square on the left side:
(t + 1)(t + 1) = 121

Calculate the square root of the right side: 11

Break this problem into two subproblems by setting 
(t + 1) equal to 11 and -11.

Subproblem 1
t + 1 = 11

Simplifying
t + 1 = 11

Reorder the terms:
1 + t = 11

Solving
1 + t = 11

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = 11 + -1

Combine like terms: 1 + -1 = 0
0 + t = 11 + -1
t = 11 + -1

Combine like terms: 11 + -1 = 10
t = 10

Simplifying
t = 10

Subproblem 2
t + 1 = -11

Simplifying
t + 1 = -11

Reorder the terms:
1 + t = -11

Solving
1 + t = -11

Solving for variable 't'.

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

Add '-1' to each side of the equation.
1 + -1 + t = -11 + -1

Combine like terms: 1 + -1 = 0
0 + t = -11 + -1
t = -11 + -1

Combine like terms: -11 + -1 = -12
t = -12

Simplifying
t = -12

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {10, -12}