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.
(-6 + -1t)(1 + -1t) = 0

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

Simplifying
1 + -1t = 0

Solving
1 + -1t = 0

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

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

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

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

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

Simplifying
t = 1
Solution
t = {-6, 1}