4u^2=-13u-3

Solution for 4u^2=-13u-3 equation:

Simplifying
4u2 = -13u + -3

Reorder the terms:
4u2 = -3 + -13u

Solving
4u2 = -3 + -13u

Solving for variable 'u'.

Reorder the terms:
3 + 13u + 4u2 = -3 + -13u + 3 + 13u

Reorder the terms:
3 + 13u + 4u2 = -3 + 3 + -13u + 13u

Combine like terms: -3 + 3 = 0
3 + 13u + 4u2 = 0 + -13u + 13u
3 + 13u + 4u2 = -13u + 13u

Combine like terms: -13u + 13u = 0
3 + 13u + 4u2 = 0

Factor a trinomial.
(3 + u)(1 + 4u) = 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 '(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 = {-3, -0.25}