t^2=9t-18

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

Simplifying
t2 = 9t + -18

Reorder the terms:
t2 = -18 + 9t

Solving
t2 = -18 + 9t

Solving for variable 't'.

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

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

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

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

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

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

Simplifying
3 + -1t = 0

Solving
3 + -1t = 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 + -1t = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1t = 0 + -3
-1t = 0 + -3

Combine like terms: 0 + -3 = -3
-1t = -3

Divide each side by '-1'.
t = 3

Simplifying
t = 3
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 = {3, 6}