(5u+7)(u+5)=23

Solution for (5u+7)(u+5)=23 equation:

Simplifying
(5u + 7)(u + 5) = 23

Reorder the terms:
(7 + 5u)(u + 5) = 23

Reorder the terms:
(7 + 5u)(5 + u) = 23

Multiply (7 + 5u) * (5 + u)
(7(5 + u) + 5u * (5 + u)) = 23
((5 * 7 + u * 7) + 5u * (5 + u)) = 23
((35 + 7u) + 5u * (5 + u)) = 23
(35 + 7u + (5 * 5u + u * 5u)) = 23
(35 + 7u + (25u + 5u2)) = 23

Combine like terms: 7u + 25u = 32u
(35 + 32u + 5u2) = 23

Solving
35 + 32u + 5u2 = 23

Solving for variable 'u'.

Reorder the terms:
35 + -23 + 32u + 5u2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32u + 5u2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32u + 5u2 = 0

Factor a trinomial.
(6 + u)(2 + 5u) = 0

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 + 5u)' equal to zero and attempt to solve:

Simplifying
2 + 5u = 0

Solving
2 + 5u = 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 + 5u = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5u = 0 + -2
5u = 0 + -2

Combine like terms: 0 + -2 = -2
5u = -2

Divide each side by '5'.
u = -0.4

Simplifying
u = -0.4
Solution
u = {-6, -0.4}