-2t^2+12t+9=1

Solution for -2t^2+12t+9=1 equation:

Simplifying
-2t2 + 12t + 9 = 1

Reorder the terms:
9 + 12t + -2t2 = 1

Solving
9 + 12t + -2t2 = 1

Solving for variable 't'.

Reorder the terms:
9 + -1 + 12t + -2t2 = 1 + -1

Combine like terms: 9 + -1 = 8
8 + 12t + -2t2 = 1 + -1

Combine like terms: 1 + -1 = 0
8 + 12t + -2t2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 6t + -1t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + 6t + -1t2)' equal to zero and attempt to solve:

Simplifying
4 + 6t + -1t2 = 0

Solving
4 + 6t + -1t2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + -6t + t2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -6t + 4 + t2 = 0 + 4

Reorder the terms:
-4 + 4 + -6t + t2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -6t + t2 = 0 + 4
-6t + t2 = 0 + 4

Combine like terms: 0 + 4 = 4
-6t + t2 = 4

The t term is -6t.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6t + 9 + t2 = 4 + 9

Reorder the terms:
9 + -6t + t2 = 4 + 9

Combine like terms: 4 + 9 = 13
9 + -6t + t2 = 13

Factor a perfect square on the left side:
(t + -3)(t + -3) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(t + -3) equal to 3.605551275 and -3.605551275.

Subproblem 1
t + -3 = 3.605551275

Simplifying
t + -3 = 3.605551275

Reorder the terms:
-3 + t = 3.605551275

Solving
-3 + t = 3.605551275

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = 3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + t = 3.605551275 + 3
t = 3.605551275 + 3

Combine like terms: 3.605551275 + 3 = 6.605551275
t = 6.605551275

Simplifying
t = 6.605551275

Subproblem 2
t + -3 = -3.605551275

Simplifying
t + -3 = -3.605551275

Reorder the terms:
-3 + t = -3.605551275

Solving
-3 + t = -3.605551275

Solving for variable 't'.

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

Add '3' to each side of the equation.
-3 + 3 + t = -3.605551275 + 3

Combine like terms: -3 + 3 = 0
0 + t = -3.605551275 + 3
t = -3.605551275 + 3

Combine like terms: -3.605551275 + 3 = -0.605551275
t = -0.605551275

Simplifying
t = -0.605551275

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {6.605551275, -0.605551275}
Solution
t = {6.605551275, -0.605551275}