-t^2-9t=18

Solution for -t^2-9t=18 equation:

Simplifying
-1t2 + -9t = 18

Reorder the terms:
-9t + -1t2 = 18

Solving
-9t + -1t2 = 18

Solving for variable 't'.

Reorder the terms:
-18 + -9t + -1t2 = 18 + -18

Combine like terms: 18 + -18 = 0
-18 + -9t + -1t2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(18 + 9t + t2) = 0

Factor a trinomial.
-1((6 + t)(3 + t)) = 0

Ignore the factor -1.
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 '(3 + t)' equal to zero and attempt to solve:

Simplifying
3 + t = 0

Solving
3 + t = 0

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 = 0 + -3

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

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

Simplifying
t = -3
Solution
t = {-6, -3}