5u=2u^2-3

Solution for 5u=2u^2-3 equation:

Simplifying
5u = 2u2 + -3

Reorder the terms:
5u = -3 + 2u2

Solving
5u = -3 + 2u2

Solving for variable 'u'.

Reorder the terms:
3 + 5u + -2u2 = -3 + 2u2 + 3 + -2u2

Reorder the terms:
3 + 5u + -2u2 = -3 + 3 + 2u2 + -2u2

Combine like terms: -3 + 3 = 0
3 + 5u + -2u2 = 0 + 2u2 + -2u2
3 + 5u + -2u2 = 2u2 + -2u2

Combine like terms: 2u2 + -2u2 = 0
3 + 5u + -2u2 = 0

Factor a trinomial.
(3 + -1u)(1 + 2u) = 0

Subproblem 1
Set the factor '(3 + -1u)' equal to zero and attempt to solve:

Simplifying
3 + -1u = 0

Solving
3 + -1u = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1u = 0 + -3
-1u = 0 + -3

Combine like terms: 0 + -3 = -3
-1u = -3

Divide each side by '-1'.
u = 3

Simplifying
u = 3
Subproblem 2
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
Solution
u = {3, -0.5}