t^2=5t-6

Solution for t^2=5t-6 equation:

Simplifying
t2 = 5t + -6

Reorder the terms:
t2 = -6 + 5t

Solving
t2 = -6 + 5t

Solving for variable 't'.

Reorder the terms:
6 + -5t + t2 = -6 + 5t + 6 + -5t

Reorder the terms:
6 + -5t + t2 = -6 + 6 + 5t + -5t

Combine like terms: -6 + 6 = 0
6 + -5t + t2 = 0 + 5t + -5t
6 + -5t + t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
6 + -5t + t2 = 0

Factor a trinomial.
(2 + -1t)(3 + -1t) = 0

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

Simplifying
2 + -1t = 0

Solving
2 + -1t = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1t = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1t = 0 + -2
-1t = 0 + -2

Combine like terms: 0 + -2 = -2
-1t = -2

Divide each side by '-1'.
t = 2

Simplifying
t = 2
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 = {2, 3}