t^2=2t^2-5t+6

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

Simplifying
t2 = 2t2 + -5t + 6

Reorder the terms:
t2 = 6 + -5t + 2t2

Solving
t2 = 6 + -5t + 2t2

Solving for variable 't'.

Reorder the terms:
-6 + 5t + t2 + -2t2 = 6 + -5t + 2t2 + -6 + 5t + -2t2

Combine like terms: t2 + -2t2 = -1t2
-6 + 5t + -1t2 = 6 + -5t + 2t2 + -6 + 5t + -2t2

Reorder the terms:
-6 + 5t + -1t2 = 6 + -6 + -5t + 5t + 2t2 + -2t2

Combine like terms: 6 + -6 = 0
-6 + 5t + -1t2 = 0 + -5t + 5t + 2t2 + -2t2
-6 + 5t + -1t2 = -5t + 5t + 2t2 + -2t2

Combine like terms: -5t + 5t = 0
-6 + 5t + -1t2 = 0 + 2t2 + -2t2
-6 + 5t + -1t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
-6 + 5t + -1t2 = 0

Factor a trinomial.
(-3 + t)(2 + -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 '(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
Solution
t = {3, 2}