3u^2-8u+21=32

Solution for 3u^2-8u+21=32 equation:

Simplifying
3u2 + -8u + 21 = 32

Reorder the terms:
21 + -8u + 3u2 = 32

Solving
21 + -8u + 3u2 = 32

Solving for variable 'u'.

Reorder the terms:
21 + -32 + -8u + 3u2 = 32 + -32

Combine like terms: 21 + -32 = -11
-11 + -8u + 3u2 = 32 + -32

Combine like terms: 32 + -32 = 0
-11 + -8u + 3u2 = 0

Factor a trinomial.
(-1 + -1u)(11 + -3u) = 0

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

Simplifying
-1 + -1u = 0

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

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

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

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

Simplifying
u = -1
Subproblem 2
Set the factor '(11 + -3u)' equal to zero and attempt to solve:

Simplifying
11 + -3u = 0

Solving
11 + -3u = 0

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

Add '-11' to each side of the equation.
11 + -11 + -3u = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -3u = 0 + -11
-3u = 0 + -11

Combine like terms: 0 + -11 = -11
-3u = -11

Divide each side by '-3'.
u = 3.666666667

Simplifying
u = 3.666666667
Solution
u = {-1, 3.666666667}