(m+3)x(m+5)=

Solution for (m+3)x(m+5)= equation:

Simplifying
(m + 3) * x(m + 5) = 0

Reorder the terms:
(3 + m) * x(m + 5) = 0

Reorder the terms:
(3 + m) * x(5 + m) = 0

Reorder the terms for easier multiplication:
x(3 + m)(5 + m) = 0

Multiply (3 + m) * (5 + m)
x(3(5 + m) + m(5 + m)) = 0
x((5 * 3 + m * 3) + m(5 + m)) = 0
x((15 + 3m) + m(5 + m)) = 0
x(15 + 3m + (5 * m + m * m)) = 0
x(15 + 3m + (5m + m2)) = 0

Combine like terms: 3m + 5m = 8m
x(15 + 8m + m2) = 0
(15 * x + 8m * x + m2 * x) = 0

Reorder the terms:
(8mx + m2x + 15x) = 0
(8mx + m2x + 15x) = 0

Solving
8mx + m2x + 15x = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(8m + m2 + 15) = 0

Factor a trinomial.
x((m + 3)(m + 5)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Add '-1x' to each side of the equation.
x + -1x = 0 + -1x
Remove the zero:
0 = -1x

Simplifying
0 = -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 2
Set the factor '(m + 3)' equal to zero and attempt to solve:

Simplifying
m + 3 = 0

Reorder the terms:
3 + m = 0

Solving
3 + m = 0

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

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

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

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

Simplifying
m = -3
Subproblem 3
Set the factor '(m + 5)' equal to zero and attempt to solve:

Simplifying
m + 5 = 0

Reorder the terms:
5 + m = 0

Solving
5 + m = 0

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

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

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

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

Simplifying
m = -5
Solution
m = {-3, -5}