4t^2=4t-1

Solution for 4t^2=4t-1 equation:

Simplifying
4t2 = 4t + -1

Reorder the terms:
4t2 = -1 + 4t

Solving
4t2 = -1 + 4t

Solving for variable 't'.

Reorder the terms:
1 + -4t + 4t2 = -1 + 4t + 1 + -4t

Reorder the terms:
1 + -4t + 4t2 = -1 + 1 + 4t + -4t

Combine like terms: -1 + 1 = 0
1 + -4t + 4t2 = 0 + 4t + -4t
1 + -4t + 4t2 = 4t + -4t

Combine like terms: 4t + -4t = 0
1 + -4t + 4t2 = 0

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

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

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Subproblem 2
Set the factor '(1 + -2t)' equal to zero and attempt to solve:

Simplifying
1 + -2t = 0

Solving
1 + -2t = 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 + -2t = 0 + -1

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

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

Divide each side by '-2'.
t = 0.5

Simplifying
t = 0.5
Solution
t = {0.5, 0.5}