(k-2)(k-3)=56

Solution for (k-2)(k-3)=56 equation:

Simplifying
(k + -2)(k + -3) = 56

Reorder the terms:
(-2 + k)(k + -3) = 56

Reorder the terms:
(-2 + k)(-3 + k) = 56

Multiply (-2 + k) * (-3 + k)
(-2(-3 + k) + k(-3 + k)) = 56
((-3 * -2 + k * -2) + k(-3 + k)) = 56
((6 + -2k) + k(-3 + k)) = 56
(6 + -2k + (-3 * k + k * k)) = 56
(6 + -2k + (-3k + k2)) = 56

Combine like terms: -2k + -3k = -5k
(6 + -5k + k2) = 56

Solving
6 + -5k + k2 = 56

Solving for variable 'k'.

Reorder the terms:
6 + -56 + -5k + k2 = 56 + -56

Combine like terms: 6 + -56 = -50
-50 + -5k + k2 = 56 + -56

Combine like terms: 56 + -56 = 0
-50 + -5k + k2 = 0

Factor a trinomial.
(-5 + -1k)(10 + -1k) = 0

Subproblem 1
Set the factor '(-5 + -1k)' equal to zero and attempt to solve:

Simplifying
-5 + -1k = 0

Solving
-5 + -1k = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1k = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1k = 0 + 5
-1k = 0 + 5

Combine like terms: 0 + 5 = 5
-1k = 5

Divide each side by '-1'.
k = -5

Simplifying
k = -5
Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {-5, 10}