(m+1)(m-4)=0

Solution for (m+1)(m-4)=0 equation:

Simplifying
(m + 1)(m + -4) = 0

Reorder the terms:
(1 + m)(m + -4) = 0

Reorder the terms:
(1 + m)(-4 + m) = 0

Multiply (1 + m) * (-4 + m)
(1(-4 + m) + m(-4 + m)) = 0
((-4 * 1 + m * 1) + m(-4 + m)) = 0
((-4 + 1m) + m(-4 + m)) = 0
(-4 + 1m + (-4 * m + m * m)) = 0
(-4 + 1m + (-4m + m2)) = 0

Combine like terms: 1m + -4m = -3m
(-4 + -3m + m2) = 0

Solving
-4 + -3m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-1 + -1m)(4 + -1m) = 0

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

Simplifying
-1 + -1m = 0

Solving
-1 + -1m = 0

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

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

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

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

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

Simplifying
m = -1
Subproblem 2
Set the factor '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {-1, 4}