2u^2=-5u-3

Solution for 2u^2=-5u-3 equation:

Simplifying
2u2 = -5u + -3

Reorder the terms:
2u2 = -3 + -5u

Solving
2u2 = -3 + -5u

Solving for variable 'u'.

Reorder the terms:
3 + 5u + 2u2 = -3 + -5u + 3 + 5u

Reorder the terms:
3 + 5u + 2u2 = -3 + 3 + -5u + 5u

Combine like terms: -3 + 3 = 0
3 + 5u + 2u2 = 0 + -5u + 5u
3 + 5u + 2u2 = -5u + 5u

Combine like terms: -5u + 5u = 0
3 + 5u + 2u2 = 0

Factor a trinomial.
(3 + 2u)(1 + u) = 0

Subproblem 1
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
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 = {-1.5, -1}