5u^2-2=-3u

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

Simplifying
5u2 + -2 = -3u

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

Solving
-2 + 5u2 = -3u

Solving for variable 'u'.

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

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

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

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

Simplifying
-1 + -1u = 0

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

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

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

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

Simplifying
u = -1
Subproblem 2
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
Solution
u = {-1, 0.4}