4u^2=-9u-2

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

Simplifying
4u2 = -9u + -2

Reorder the terms:
4u2 = -2 + -9u

Solving
4u2 = -2 + -9u

Solving for variable 'u'.

Reorder the terms:
2 + 9u + 4u2 = -2 + -9u + 2 + 9u

Reorder the terms:
2 + 9u + 4u2 = -2 + 2 + -9u + 9u

Combine like terms: -2 + 2 = 0
2 + 9u + 4u2 = 0 + -9u + 9u
2 + 9u + 4u2 = -9u + 9u

Combine like terms: -9u + 9u = 0
2 + 9u + 4u2 = 0

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

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

Simplifying
2 + u = 0

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

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

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

Simplifying
u = -2
Subproblem 2
Set the factor '(1 + 4u)' equal to zero and attempt to solve:

Simplifying
1 + 4u = 0

Solving
1 + 4u = 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 + 4u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4u = 0 + -1
4u = 0 + -1

Combine like terms: 0 + -1 = -1
4u = -1

Divide each side by '4'.
u = -0.25

Simplifying
u = -0.25
Solution
u = {-2, -0.25}