3u^2=14u+5

Solution for 3u^2=14u+5 equation:

Simplifying
3u2 = 14u + 5

Reorder the terms:
3u2 = 5 + 14u

Solving
3u2 = 5 + 14u

Solving for variable 'u'.

Reorder the terms:
-5 + -14u + 3u2 = 5 + 14u + -5 + -14u

Reorder the terms:
-5 + -14u + 3u2 = 5 + -5 + 14u + -14u

Combine like terms: 5 + -5 = 0
-5 + -14u + 3u2 = 0 + 14u + -14u
-5 + -14u + 3u2 = 14u + -14u

Combine like terms: 14u + -14u = 0
-5 + -14u + 3u2 = 0

Factor a trinomial.
(-1 + -3u)(5 + -1u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5 + -1u)' equal to zero and attempt to solve:

Simplifying
5 + -1u = 0

Solving
5 + -1u = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1u = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1u = 0 + -5
-1u = 0 + -5

Combine like terms: 0 + -5 = -5
-1u = -5

Divide each side by '-1'.
u = 5

Simplifying
u = 5
Solution
u = {-0.3333333333, 5}