2t^2=5t-2

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

Simplifying
2t2 = 5t + -2

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

Solving
2t2 = -2 + 5t

Solving for variable 't'.

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

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

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

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

Factor a trinomial.
(1 + -2t)(2 + -1t) = 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 '(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 = {0.5, 2}