(k-3)(k-3)=(2)(k+1)

Solution for (k-3)(k-3)=(2)(k+1) equation:

Simplifying
(k + -3)(k + -3) = (2)(k + 1)

Reorder the terms:
(-3 + k)(k + -3) = (2)(k + 1)

Reorder the terms:
(-3 + k)(-3 + k) = (2)(k + 1)

Multiply (-3 + k) * (-3 + k)
(-3(-3 + k) + k(-3 + k)) = (2)(k + 1)
((-3 * -3 + k * -3) + k(-3 + k)) = (2)(k + 1)
((9 + -3k) + k(-3 + k)) = (2)(k + 1)
(9 + -3k + (-3 * k + k * k)) = (2)(k + 1)
(9 + -3k + (-3k + k2)) = (2)(k + 1)

Combine like terms: -3k + -3k = -6k
(9 + -6k + k2) = (2)(k + 1)

Reorder the terms:
9 + -6k + k2 = 2(1 + k)
9 + -6k + k2 = (1 * 2 + k * 2)
9 + -6k + k2 = (2 + 2k)

Solving
9 + -6k + k2 = 2 + 2k

Solving for variable 'k'.

Reorder the terms:
9 + -2 + -6k + -2k + k2 = 2 + 2k + -2 + -2k

Combine like terms: 9 + -2 = 7
7 + -6k + -2k + k2 = 2 + 2k + -2 + -2k

Combine like terms: -6k + -2k = -8k
7 + -8k + k2 = 2 + 2k + -2 + -2k

Reorder the terms:
7 + -8k + k2 = 2 + -2 + 2k + -2k

Combine like terms: 2 + -2 = 0
7 + -8k + k2 = 0 + 2k + -2k
7 + -8k + k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
7 + -8k + k2 = 0

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

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

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

Simplifying
7 + -1k = 0

Solving
7 + -1k = 0

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

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

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

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

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

Simplifying
k = 7
Solution
k = {1, 7}