(5m+7)(m+5)=23

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

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

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

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

Multiply (7 + 5m) * (5 + m)
(7(5 + m) + 5m * (5 + m)) = 23
((5 * 7 + m * 7) + 5m * (5 + m)) = 23
((35 + 7m) + 5m * (5 + m)) = 23
(35 + 7m + (5 * 5m + m * 5m)) = 23
(35 + 7m + (25m + 5m2)) = 23

Combine like terms: 7m + 25m = 32m
(35 + 32m + 5m2) = 23

Solving
35 + 32m + 5m2 = 23

Solving for variable 'm'.

Reorder the terms:
35 + -23 + 32m + 5m2 = 23 + -23

Combine like terms: 35 + -23 = 12
12 + 32m + 5m2 = 23 + -23

Combine like terms: 23 + -23 = 0
12 + 32m + 5m2 = 0

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

Subproblem 1
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

Add '-6' to each side of the equation.
6 + -6 + m = 0 + -6

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

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

Simplifying
m = -6
Subproblem 2
Set the factor '(2 + 5m)' equal to zero and attempt to solve:

Simplifying
2 + 5m = 0

Solving
2 + 5m = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5m = 0 + -2

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

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

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

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