3u^2+4=-7u

Solution for 3u^2+4=-7u equation:

Simplifying
3u2 + 4 = -7u

Reorder the terms:
4 + 3u2 = -7u

Solving
4 + 3u2 = -7u

Solving for variable 'u'.

Reorder the terms:
4 + 7u + 3u2 = -7u + 7u

Combine like terms: -7u + 7u = 0
4 + 7u + 3u2 = 0

Factor a trinomial.
(4 + 3u)(1 + u) = 0

Subproblem 1
Set the factor '(4 + 3u)' equal to zero and attempt to solve:

Simplifying
4 + 3u = 0

Solving
4 + 3u = 0

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

Add '-4' to each side of the equation.
4 + -4 + 3u = 0 + -4

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

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

Divide each side by '3'.
u = -1.333333333

Simplifying
u = -1.333333333
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 = {-1.333333333, -1}