3u^2=6-7u

Solution for 3u^2=6-7u equation:

Simplifying
3u2 = 6 + -7u

Solving
3u2 = 6 + -7u

Solving for variable 'u'.

Reorder the terms:
-6 + 7u + 3u2 = 6 + -7u + -6 + 7u

Reorder the terms:
-6 + 7u + 3u2 = 6 + -6 + -7u + 7u

Combine like terms: 6 + -6 = 0
-6 + 7u + 3u2 = 0 + -7u + 7u
-6 + 7u + 3u2 = -7u + 7u

Combine like terms: -7u + 7u = 0
-6 + 7u + 3u2 = 0

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

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

Simplifying
-3 + -1u = 0

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

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

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

Divide each side by '-1'.
u = -3

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

Simplifying
2 + -3u = 0

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

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

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

Divide each side by '-3'.
u = 0.6666666667

Simplifying
u = 0.6666666667
Solution
u = {-3, 0.6666666667}