t^2=2t-1

Solution for t^2=2t-1 equation:

Simplifying
t2 = 2t + -1

Reorder the terms:
t2 = -1 + 2t

Solving
t2 = -1 + 2t

Solving for variable 't'.

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

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

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

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

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

Subproblem 1
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
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 = {1, 1}