4u^2=-12u-5

Solution for 4u^2=-12u-5 equation:

Simplifying
4u2 = -12u + -5

Reorder the terms:
4u2 = -5 + -12u

Solving
4u2 = -5 + -12u

Solving for variable 'u'.

Reorder the terms:
5 + 12u + 4u2 = -5 + -12u + 5 + 12u

Reorder the terms:
5 + 12u + 4u2 = -5 + 5 + -12u + 12u

Combine like terms: -5 + 5 = 0
5 + 12u + 4u2 = 0 + -12u + 12u
5 + 12u + 4u2 = -12u + 12u

Combine like terms: -12u + 12u = 0
5 + 12u + 4u2 = 0

Factor a trinomial.
(5 + 2u)(1 + 2u) = 0

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

Simplifying
5 + 2u = 0

Solving
5 + 2u = 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 + 2u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2u = 0 + -5
2u = 0 + -5

Combine like terms: 0 + -5 = -5
2u = -5

Divide each side by '2'.
u = -2.5

Simplifying
u = -2.5
Subproblem 2
Set the factor '(1 + 2u)' equal to zero and attempt to solve:

Simplifying
1 + 2u = 0

Solving
1 + 2u = 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 + 2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2u = 0 + -1
2u = 0 + -1

Combine like terms: 0 + -1 = -1
2u = -1

Divide each side by '2'.
u = -0.5

Simplifying
u = -0.5
Solution
u = {-2.5, -0.5}