-t^2=36-12t

Solution for -t^2=36-12t equation:

Simplifying
-1t2 = 36 + -12t

Solving
-1t2 = 36 + -12t

Solving for variable 't'.

Reorder the terms:
-36 + 12t + -1t2 = 36 + -12t + -36 + 12t

Reorder the terms:
-36 + 12t + -1t2 = 36 + -36 + -12t + 12t

Combine like terms: 36 + -36 = 0
-36 + 12t + -1t2 = 0 + -12t + 12t
-36 + 12t + -1t2 = -12t + 12t

Combine like terms: -12t + 12t = 0
-36 + 12t + -1t2 = 0

Factor a trinomial.
(-6 + t)(6 + -1t) = 0

Subproblem 1
Set the factor '(-6 + t)' equal to zero and attempt to solve:

Simplifying
-6 + t = 0

Solving
-6 + t = 0

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

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

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

Combine like terms: 0 + 6 = 6
t = 6

Simplifying
t = 6
Subproblem 2
Set the factor '(6 + -1t)' equal to zero and attempt to solve:

Simplifying
6 + -1t = 0

Solving
6 + -1t = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1t = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1t = 0 + -6
-1t = 0 + -6

Combine like terms: 0 + -6 = -6
-1t = -6

Divide each side by '-1'.
t = 6

Simplifying
t = 6
Solution
t = {6, 6}