12u+2u^2=224

Solution for 12u+2u^2=224 equation:

Simplifying
12u + 2u2 = 224

Solving
12u + 2u2 = 224

Solving for variable 'u'.

Reorder the terms:
-224 + 12u + 2u2 = 224 + -224

Combine like terms: 224 + -224 = 0
-224 + 12u + 2u2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-112 + 6u + u2) = 0

Factor a trinomial.
2((-14 + -1u)(8 + -1u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-14 + -1u)' equal to zero and attempt to solve:

Simplifying
-14 + -1u = 0

Solving
-14 + -1u = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1u = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1u = 0 + 14
-1u = 0 + 14

Combine like terms: 0 + 14 = 14
-1u = 14

Divide each side by '-1'.
u = -14

Simplifying
u = -14
Subproblem 2
Set the factor '(8 + -1u)' equal to zero and attempt to solve:

Simplifying
8 + -1u = 0

Solving
8 + -1u = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1u = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1u = 0 + -8
-1u = 0 + -8

Combine like terms: 0 + -8 = -8
-1u = -8

Divide each side by '-1'.
u = 8

Simplifying
u = 8
Solution
u = {-14, 8}