4u^2+5=-9u

Solution for 4u^2+5=-9u equation:

Simplifying
4u2 + 5 = -9u

Reorder the terms:
5 + 4u2 = -9u

Solving
5 + 4u2 = -9u

Solving for variable 'u'.

Reorder the terms:
5 + 9u + 4u2 = -9u + 9u

Combine like terms: -9u + 9u = 0
5 + 9u + 4u2 = 0

Factor a trinomial.
(5 + 4u)(1 + u) = 0

Subproblem 1
Set the factor '(5 + 4u)' equal to zero and attempt to solve:

Simplifying
5 + 4u = 0

Solving
5 + 4u = 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 + 4u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 4u = 0 + -5
4u = 0 + -5

Combine like terms: 0 + -5 = -5
4u = -5

Divide each side by '4'.
u = -1.25

Simplifying
u = -1.25
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 = {-1.25, -1}