(7+u)(4u+6)=0

Solution for (7+u)(4u+6)=0 equation:

Simplifying
(7 + u)(4u + 6) = 0

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

Multiply (7 + u) * (6 + 4u)
(7(6 + 4u) + u(6 + 4u)) = 0
((6 * 7 + 4u * 7) + u(6 + 4u)) = 0
((42 + 28u) + u(6 + 4u)) = 0
(42 + 28u + (6 * u + 4u * u)) = 0
(42 + 28u + (6u + 4u2)) = 0

Combine like terms: 28u + 6u = 34u
(42 + 34u + 4u2) = 0

Solving
42 + 34u + 4u2 = 0

Solving for variable 'u'.

Factor out the Greatest Common Factor (GCF), '2'.
2(21 + 17u + 2u2) = 0

Factor a trinomial.
2((7 + u)(3 + 2u)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(7 + u)' equal to zero and attempt to solve:

Simplifying
7 + u = 0

Solving
7 + u = 0

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

Add '-7' to each side of the equation.
7 + -7 + u = 0 + -7

Combine like terms: 7 + -7 = 0
0 + u = 0 + -7
u = 0 + -7

Combine like terms: 0 + -7 = -7
u = -7

Simplifying
u = -7
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 = {-7, -1.5}