(3u-2)(6+u)=0

Solution for (3u-2)(6+u)=0 equation:

Simplifying
(3u + -2)(6 + u) = 0

Reorder the terms:
(-2 + 3u)(6 + u) = 0

Multiply (-2 + 3u) * (6 + u)
(-2(6 + u) + 3u * (6 + u)) = 0
((6 * -2 + u * -2) + 3u * (6 + u)) = 0
((-12 + -2u) + 3u * (6 + u)) = 0
(-12 + -2u + (6 * 3u + u * 3u)) = 0
(-12 + -2u + (18u + 3u2)) = 0

Combine like terms: -2u + 18u = 16u
(-12 + 16u + 3u2) = 0

Solving
-12 + 16u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(2 + -3u) = 0

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

Simplifying
2 + -3u = 0

Solving
2 + -3u = 0

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

Add '-2' to each side of the equation.
2 + -2 + -3u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3u = 0 + -2
-3u = 0 + -2

Combine like terms: 0 + -2 = -2
-3u = -2

Divide each side by '-3'.
u = 0.6666666667

Simplifying
u = 0.6666666667
Solution
u = {-6, 0.6666666667}