(6-u)(4+2u)=0

Solution for (6-u)(4+2u)=0 equation:

Simplifying
(6 + -1u)(4 + 2u) = 0

Multiply (6 + -1u) * (4 + 2u)
(6(4 + 2u) + -1u * (4 + 2u)) = 0
((4 * 6 + 2u * 6) + -1u * (4 + 2u)) = 0
((24 + 12u) + -1u * (4 + 2u)) = 0
(24 + 12u + (4 * -1u + 2u * -1u)) = 0
(24 + 12u + (-4u + -2u2)) = 0

Combine like terms: 12u + -4u = 8u
(24 + 8u + -2u2) = 0

Solving
24 + 8u + -2u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(12 + 4u + -1u2) = 0

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

Ignore the factor 2.
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 + u)' equal to zero and attempt to solve:

Simplifying
2 + u = 0

Solving
2 + u = 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 + u = 0 + -2

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

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

Simplifying
u = -2
Solution
u = {6, -2}