u^2=54-3u

Solution for u^2=54-3u equation:

Simplifying
u2 = 54 + -3u

Solving
u2 = 54 + -3u

Solving for variable 'u'.

Reorder the terms:
-54 + 3u + u2 = 54 + -3u + -54 + 3u

Reorder the terms:
-54 + 3u + u2 = 54 + -54 + -3u + 3u

Combine like terms: 54 + -54 = 0
-54 + 3u + u2 = 0 + -3u + 3u
-54 + 3u + u2 = -3u + 3u

Combine like terms: -3u + 3u = 0
-54 + 3u + u2 = 0

Factor a trinomial.
(-9 + -1u)(6 + -1u) = 0

Subproblem 1
Set the factor '(-9 + -1u)' equal to zero and attempt to solve:

Simplifying
-9 + -1u = 0

Solving
-9 + -1u = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1u = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1u = 0 + 9
-1u = 0 + 9

Combine like terms: 0 + 9 = 9
-1u = 9

Divide each side by '-1'.
u = -9

Simplifying
u = -9
Subproblem 2
Set the factor '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {-9, 6}