5u^2+6=-17u

Solution for 5u^2+6=-17u equation:

Simplifying
5u2 + 6 = -17u

Reorder the terms:
6 + 5u2 = -17u

Solving
6 + 5u2 = -17u

Solving for variable 'u'.

Reorder the terms:
6 + 17u + 5u2 = -17u + 17u

Combine like terms: -17u + 17u = 0
6 + 17u + 5u2 = 0

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

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

Simplifying
3 + u = 0

Solving
3 + u = 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 + u = 0 + -3

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

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

Simplifying
u = -3
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 = {-3, -0.4}