(m+7)(m-3)=0

Solution for (m+7)(m-3)=0 equation:

Simplifying
(m + 7)(m + -3) = 0

Reorder the terms:
(7 + m)(m + -3) = 0

Reorder the terms:
(7 + m)(-3 + m) = 0

Multiply (7 + m) * (-3 + m)
(7(-3 + m) + m(-3 + m)) = 0
((-3 * 7 + m * 7) + m(-3 + m)) = 0
((-21 + 7m) + m(-3 + m)) = 0
(-21 + 7m + (-3 * m + m * m)) = 0
(-21 + 7m + (-3m + m2)) = 0

Combine like terms: 7m + -3m = 4m
(-21 + 4m + m2) = 0

Solving
-21 + 4m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-7 + -1m)(3 + -1m) = 0

Subproblem 1
Set the factor '(-7 + -1m)' equal to zero and attempt to solve:

Simplifying
-7 + -1m = 0

Solving
-7 + -1m = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1m = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1m = 0 + 7
-1m = 0 + 7

Combine like terms: 0 + 7 = 7
-1m = 7

Divide each side by '-1'.
m = -7

Simplifying
m = -7
Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 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 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {-7, 3}