0=t^2-6t+9

Solution for 0=t^2-6t+9 equation:

Simplifying
0 = t2 + -6t + 9

Reorder the terms:
0 = 9 + -6t + t2

Solving
0 = 9 + -6t + t2

Solving for variable 't'.

Combine like terms: 0 + -9 = -9
-9 + 6t + -1t2 = 9 + -6t + t2 + -9 + 6t + -1t2

Reorder the terms:
-9 + 6t + -1t2 = 9 + -9 + -6t + 6t + t2 + -1t2

Combine like terms: 9 + -9 = 0
-9 + 6t + -1t2 = 0 + -6t + 6t + t2 + -1t2
-9 + 6t + -1t2 = -6t + 6t + t2 + -1t2

Combine like terms: -6t + 6t = 0
-9 + 6t + -1t2 = 0 + t2 + -1t2
-9 + 6t + -1t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
-9 + 6t + -1t2 = 0

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

Subproblem 1
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
Subproblem 2
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
Solution
t = {3, 3}