(u-2)(u-9)=-6

Solution for (u-2)(u-9)=-6 equation:

Simplifying
(u + -2)(u + -9) = -6

Reorder the terms:
(-2 + u)(u + -9) = -6

Reorder the terms:
(-2 + u)(-9 + u) = -6

Multiply (-2 + u) * (-9 + u)
(-2(-9 + u) + u(-9 + u)) = -6
((-9 * -2 + u * -2) + u(-9 + u)) = -6
((18 + -2u) + u(-9 + u)) = -6
(18 + -2u + (-9 * u + u * u)) = -6
(18 + -2u + (-9u + u2)) = -6

Combine like terms: -2u + -9u = -11u
(18 + -11u + u2) = -6

Solving
18 + -11u + u2 = -6

Solving for variable 'u'.

Reorder the terms:
18 + 6 + -11u + u2 = -6 + 6

Combine like terms: 18 + 6 = 24
24 + -11u + u2 = -6 + 6

Combine like terms: -6 + 6 = 0
24 + -11u + u2 = 0

Factor a trinomial.
(3 + -1u)(8 + -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 '(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 = {3, 8}