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

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

Simplifying
(2u + 6)(-1(2u + 3)) = 0

Reorder the terms:
(6 + 2u)(-1(2u + 3)) = 0

Reorder the terms:
(6 + 2u)(-1(3 + 2u)) = 0
(6 + 2u)((3 * -1 + 2u * -1)) = 0
(6 + 2u)((-3 + -2u)) = 0

Multiply (6 + 2u) * (-3 + -2u)
(6(-3 + -2u) + 2u * (-3 + -2u)) = 0
((-3 * 6 + -2u * 6) + 2u * (-3 + -2u)) = 0
((-18 + -12u) + 2u * (-3 + -2u)) = 0
(-18 + -12u + (-3 * 2u + -2u * 2u)) = 0
(-18 + -12u + (-6u + -4u2)) = 0

Combine like terms: -12u + -6u = -18u
(-18 + -18u + -4u2) = 0

Solving
-18 + -18u + -4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '-2'.
-2(9 + 9u + 2u2) = 0

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

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

Simplifying
3 + u = 0

Solving
3 + u = 0

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

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

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

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

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

Simplifying
3 + 2u = 0

Solving
3 + 2u = 0

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

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

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

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

Divide each side by '2'.
u = -1.5

Simplifying
u = -1.5
Solution
u = {-3, -1.5}