k^2-67=3k+3

Solution for k^2-67=3k+3 equation:

Simplifying
k2 + -67 = 3k + 3

Reorder the terms:
-67 + k2 = 3k + 3

Reorder the terms:
-67 + k2 = 3 + 3k

Solving
-67 + k2 = 3 + 3k

Solving for variable 'k'.

Reorder the terms:
-67 + -3 + -3k + k2 = 3 + 3k + -3 + -3k

Combine like terms: -67 + -3 = -70
-70 + -3k + k2 = 3 + 3k + -3 + -3k

Reorder the terms:
-70 + -3k + k2 = 3 + -3 + 3k + -3k

Combine like terms: 3 + -3 = 0
-70 + -3k + k2 = 0 + 3k + -3k
-70 + -3k + k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-70 + -3k + k2 = 0

Factor a trinomial.
(-7 + -1k)(10 + -1k) = 0

Subproblem 1
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
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 = {-7, 10}