3u^2=-7u-2

Solution for 3u^2=-7u-2 equation:

Simplifying
3u2 = -7u + -2

Reorder the terms:
3u2 = -2 + -7u

Solving
3u2 = -2 + -7u

Solving for variable 'u'.

Reorder the terms:
2 + 7u + 3u2 = -2 + -7u + 2 + 7u

Reorder the terms:
2 + 7u + 3u2 = -2 + 2 + -7u + 7u

Combine like terms: -2 + 2 = 0
2 + 7u + 3u2 = 0 + -7u + 7u
2 + 7u + 3u2 = -7u + 7u

Combine like terms: -7u + 7u = 0
2 + 7u + 3u2 = 0

Factor a trinomial.
(2 + u)(1 + 3u) = 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 + 3u)' equal to zero and attempt to solve:

Simplifying
1 + 3u = 0

Solving
1 + 3u = 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 + 3u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 3u = 0 + -1
3u = 0 + -1

Combine like terms: 0 + -1 = -1
3u = -1

Divide each side by '3'.
u = -0.3333333333

Simplifying
u = -0.3333333333
Solution
u = {-2, -0.3333333333}