k^2-6k+9=2k+2

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Solution for k^2-6k+9=2k+2 equation:


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

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

Reorder the terms:
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}

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