(m-3)(m-4)=20

Solution for (m-3)(m-4)=20 equation:

Simplifying
(m + -3)(m + -4) = 20

Reorder the terms:
(-3 + m)(m + -4) = 20

Reorder the terms:
(-3 + m)(-4 + m) = 20

Multiply (-3 + m) * (-4 + m)
(-3(-4 + m) + m(-4 + m)) = 20
((-4 * -3 + m * -3) + m(-4 + m)) = 20
((12 + -3m) + m(-4 + m)) = 20
(12 + -3m + (-4 * m + m * m)) = 20
(12 + -3m + (-4m + m2)) = 20

Combine like terms: -3m + -4m = -7m
(12 + -7m + m2) = 20

Solving
12 + -7m + m2 = 20

Solving for variable 'm'.

Reorder the terms:
12 + -20 + -7m + m2 = 20 + -20

Combine like terms: 12 + -20 = -8
-8 + -7m + m2 = 20 + -20

Combine like terms: 20 + -20 = 0
-8 + -7m + m2 = 0

Factor a trinomial.
(-1 + -1m)(8 + -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 '(8 + -1m)' equal to zero and attempt to solve:

Simplifying
8 + -1m = 0

Solving
8 + -1m = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1m = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1m = 0 + -8
-1m = 0 + -8

Combine like terms: 0 + -8 = -8
-1m = -8

Divide each side by '-1'.
m = 8

Simplifying
m = 8
Solution
m = {-1, 8}