(u-6)(u+3)=

Solution for (u-6)(u+3)= equation:

Simplifying
(u + -6)(u + 3) = 0

Reorder the terms:
(-6 + u)(u + 3) = 0

Reorder the terms:
(-6 + u)(3 + u) = 0

Multiply (-6 + u) * (3 + u)
(-6(3 + u) + u(3 + u)) = 0
((3 * -6 + u * -6) + u(3 + u)) = 0
((-18 + -6u) + u(3 + u)) = 0
(-18 + -6u + (3 * u + u * u)) = 0
(-18 + -6u + (3u + u2)) = 0

Combine like terms: -6u + 3u = -3u
(-18 + -3u + u2) = 0

Solving
-18 + -3u + u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-3 + -1u)(6 + -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 '(6 + -1u)' equal to zero and attempt to solve:

Simplifying
6 + -1u = 0

Solving
6 + -1u = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1u = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1u = 0 + -6
-1u = 0 + -6

Combine like terms: 0 + -6 = -6
-1u = -6

Divide each side by '-1'.
u = 6

Simplifying
u = 6
Solution
u = {-3, 6}