2u^2=5u-2

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

Simplifying
2u2 = 5u + -2

Reorder the terms:
2u2 = -2 + 5u

Solving
2u2 = -2 + 5u

Solving for variable 'u'.

Reorder the terms:
2 + -5u + 2u2 = -2 + 5u + 2 + -5u

Reorder the terms:
2 + -5u + 2u2 = -2 + 2 + 5u + -5u

Combine like terms: -2 + 2 = 0
2 + -5u + 2u2 = 0 + 5u + -5u
2 + -5u + 2u2 = 5u + -5u

Combine like terms: 5u + -5u = 0
2 + -5u + 2u2 = 0

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

Subproblem 1
Set the factor '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2u = 0 + -1

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

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

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-2' to each side of the equation.
2 + -2 + -1u = 0 + -2

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

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

Divide each side by '-1'.
u = 2

Simplifying
u = 2
Solution
u = {0.5, 2}