(3u-4)(6+u)=0

Solution for (3u-4)(6+u)=0 equation:

Simplifying
(3u + -4)(6 + u) = 0

Reorder the terms:
(-4 + 3u)(6 + u) = 0

Multiply (-4 + 3u) * (6 + u)
(-4(6 + u) + 3u * (6 + u)) = 0
((6 * -4 + u * -4) + 3u * (6 + u)) = 0
((-24 + -4u) + 3u * (6 + u)) = 0
(-24 + -4u + (6 * 3u + u * 3u)) = 0
(-24 + -4u + (18u + 3u2)) = 0

Combine like terms: -4u + 18u = 14u
(-24 + 14u + 3u2) = 0

Solving
-24 + 14u + 3u2 = 0

Solving for variable 'u'.

Factor a trinomial.
(-6 + -1u)(4 + -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 '(4 + -3u)' equal to zero and attempt to solve:

Simplifying
4 + -3u = 0

Solving
4 + -3u = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3u = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3u = 0 + -4
-3u = 0 + -4

Combine like terms: 0 + -4 = -4
-3u = -4

Divide each side by '-3'.
u = 1.333333333

Simplifying
u = 1.333333333
Solution
u = {-6, 1.333333333}