u^2=10u-21

Solution for u^2=10u-21 equation:

Simplifying
u2 = 10u + -21

Reorder the terms:
u2 = -21 + 10u

Solving
u2 = -21 + 10u

Solving for variable 'u'.

Reorder the terms:
21 + -10u + u2 = -21 + 10u + 21 + -10u

Reorder the terms:
21 + -10u + u2 = -21 + 21 + 10u + -10u

Combine like terms: -21 + 21 = 0
21 + -10u + u2 = 0 + 10u + -10u
21 + -10u + u2 = 10u + -10u

Combine like terms: 10u + -10u = 0
21 + -10u + u2 = 0

Factor a trinomial.
(3 + -1u)(7 + -1u) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(7 + -1u)' equal to zero and attempt to solve:

Simplifying
7 + -1u = 0

Solving
7 + -1u = 0

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

Add '-7' to each side of the equation.
7 + -7 + -1u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1u = 0 + -7
-1u = 0 + -7

Combine like terms: 0 + -7 = -7
-1u = -7

Divide each side by '-1'.
u = 7

Simplifying
u = 7
Solution
u = {3, 7}