3u^2-6=7u

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

Simplifying
3u2 + -6 = 7u

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

Solving
-6 + 3u2 = 7u

Solving for variable 'u'.

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

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

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

Subproblem 1
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
Subproblem 2
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
Solution
u = {-0.6666666667, 3}