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

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

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

Reorder the terms:
(6 + u)(-2 + 4u) = 0

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

Combine like terms: 24u + -2u = 22u
(-12 + 22u + 4u2) = 0

Solving
-12 + 22u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-6 + 11u + 2u2) = 0

Factor a trinomial.
2((-6 + -1u)(1 + -2u)) = 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 '(1 + -2u)' equal to zero and attempt to solve:

Simplifying
1 + -2u = 0

Solving
1 + -2u = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2u = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2u = 0 + -1
-2u = 0 + -1

Combine like terms: 0 + -1 = -1
-2u = -1

Divide each side by '-2'.
u = 0.5

Simplifying
u = 0.5
Solution
u = {-6, 0.5}