2u=3u^2-5

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

Simplifying
2u = 3u2 + -5

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

Solving
2u = -5 + 3u2

Solving for variable 'u'.

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

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

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

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

Factor a trinomial.
(5 + -3u)(1 + u) = 0

Subproblem 1
Set the factor '(5 + -3u)' equal to zero and attempt to solve:

Simplifying
5 + -3u = 0

Solving
5 + -3u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -3u = 0 + -5

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

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

Divide each side by '-3'.
u = 1.666666667

Simplifying
u = 1.666666667
Subproblem 2
Set the factor '(1 + u)' equal to zero and attempt to solve:

Simplifying
1 + u = 0

Solving
1 + u = 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 + u = 0 + -1

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

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

Simplifying
u = -1
Solution
u = {1.666666667, -1}