-3u=5u^2-2

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

Simplifying
-3u = 5u2 + -2

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

Solving
-3u = -2 + 5u2

Solving for variable 'u'.

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

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

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

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

Factor a trinomial.
(2 + -5u)(1 + u) = 0

Subproblem 1
Set the factor '(2 + -5u)' equal to zero and attempt to solve:

Simplifying
2 + -5u = 0

Solving
2 + -5u = 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 + -5u = 0 + -2

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

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

Divide each side by '-5'.
u = 0.4

Simplifying
u = 0.4
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 = {0.4, -1}