4t^2=5t-1

Solution for 4t^2=5t-1 equation:

Simplifying
4t2 = 5t + -1

Reorder the terms:
4t2 = -1 + 5t

Solving
4t2 = -1 + 5t

Solving for variable 't'.

Reorder the terms:
1 + -5t + 4t2 = -1 + 5t + 1 + -5t

Reorder the terms:
1 + -5t + 4t2 = -1 + 1 + 5t + -5t

Combine like terms: -1 + 1 = 0
1 + -5t + 4t2 = 0 + 5t + -5t
1 + -5t + 4t2 = 5t + -5t

Combine like terms: 5t + -5t = 0
1 + -5t + 4t2 = 0

Factor a trinomial.
(1 + -4t)(1 + -1t) = 0

Subproblem 1
Set the factor '(1 + -4t)' equal to zero and attempt to solve:

Simplifying
1 + -4t = 0

Solving
1 + -4t = 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 + -4t = 0 + -1

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

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

Divide each side by '-4'.
t = 0.25

Simplifying
t = 0.25
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 = {0.25, 1}