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

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

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

Reorder the terms:
4(-2 + u)(-1u + 6) = 0

Reorder the terms:
4(-2 + u)(6 + -1u) = 0

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

Combine like terms: 2u + 6u = 8u
4(-12 + 8u + -1u2) = 0
(-12 * 4 + 8u * 4 + -1u2 * 4) = 0
(-48 + 32u + -4u2) = 0

Solving
-48 + 32u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-12 + 8u + -1u2) = 0

Factor a trinomial.
4((-6 + u)(2 + -1u)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-6 + u)' equal to zero and attempt to solve:

Simplifying
-6 + u = 0

Solving
-6 + u = 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 + u = 0 + 6

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

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

Simplifying
u = 6
Subproblem 2
Set the factor '(2 + -1u)' equal to zero and attempt to solve:

Simplifying
2 + -1u = 0

Solving
2 + -1u = 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 + -1u = 0 + -2

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

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

Divide each side by '-1'.
u = 2

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