24u=-5+5u^2

Solution for 24u=-5+5u^2 equation:

Simplifying
24u = -5 + 5u2

Solving
24u = -5 + 5u2

Solving for variable 'u'.

Reorder the terms:
5 + 24u + -5u2 = -5 + 5u2 + 5 + -5u2

Reorder the terms:
5 + 24u + -5u2 = -5 + 5 + 5u2 + -5u2

Combine like terms: -5 + 5 = 0
5 + 24u + -5u2 = 0 + 5u2 + -5u2
5 + 24u + -5u2 = 5u2 + -5u2

Combine like terms: 5u2 + -5u2 = 0
5 + 24u + -5u2 = 0

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

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

Simplifying
5 + -1u = 0

Solving
5 + -1u = 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 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

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

Simplifying
1 + 5u = 0

Solving
1 + 5u = 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 + 5u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 5u = 0 + -1
5u = 0 + -1

Combine like terms: 0 + -1 = -1
5u = -1

Divide each side by '5'.
u = -0.2

Simplifying
u = -0.2
Solution
u = {5, -0.2}