4u^2+24u=-27

Solution for 4u^2+24u=-27 equation:

Simplifying
4u2 + 24u = -27

Reorder the terms:
24u + 4u2 = -27

Solving
24u + 4u2 = -27

Solving for variable 'u'.

Reorder the terms:
27 + 24u + 4u2 = -27 + 27

Combine like terms: -27 + 27 = 0
27 + 24u + 4u2 = 0

Factor a trinomial.
(9 + 2u)(3 + 2u) = 0

Subproblem 1
Set the factor '(9 + 2u)' equal to zero and attempt to solve:

Simplifying
9 + 2u = 0

Solving
9 + 2u = 0

Move all terms containing u to the left, all other terms to the right.

Add '-9' to each side of the equation.
9 + -9 + 2u = 0 + -9

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

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

Divide each side by '2'.
u = -4.5

Simplifying
u = -4.5
Subproblem 2
Set the factor '(3 + 2u)' equal to zero and attempt to solve:

Simplifying
3 + 2u = 0

Solving
3 + 2u = 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 + 2u = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2u = 0 + -3
2u = 0 + -3

Combine like terms: 0 + -3 = -3
2u = -3

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {-4.5, -1.5}