k^2+5k+6=(k+2)(k+6)

Solution for k^2+5k+6=(k+2)(k+6) equation:

Simplifying
k2 + 5k + 6 = (k + 2)(k + 6)

Reorder the terms:
6 + 5k + k2 = (k + 2)(k + 6)

Reorder the terms:
6 + 5k + k2 = (2 + k)(k + 6)

Reorder the terms:
6 + 5k + k2 = (2 + k)(6 + k)

Multiply (2 + k) * (6 + k)
6 + 5k + k2 = (2(6 + k) + k(6 + k))
6 + 5k + k2 = ((6 * 2 + k * 2) + k(6 + k))
6 + 5k + k2 = ((12 + 2k) + k(6 + k))
6 + 5k + k2 = (12 + 2k + (6 * k + k * k))
6 + 5k + k2 = (12 + 2k + (6k + k2))

Combine like terms: 2k + 6k = 8k
6 + 5k + k2 = (12 + 8k + k2)

Add '-1k2' to each side of the equation.
6 + 5k + k2 + -1k2 = 12 + 8k + k2 + -1k2

Combine like terms: k2 + -1k2 = 0
6 + 5k + 0 = 12 + 8k + k2 + -1k2
6 + 5k = 12 + 8k + k2 + -1k2

Combine like terms: k2 + -1k2 = 0
6 + 5k = 12 + 8k + 0
6 + 5k = 12 + 8k

Solving
6 + 5k = 12 + 8k

Solving for variable 'k'.

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

Add '-8k' to each side of the equation.
6 + 5k + -8k = 12 + 8k + -8k

Combine like terms: 5k + -8k = -3k
6 + -3k = 12 + 8k + -8k

Combine like terms: 8k + -8k = 0
6 + -3k = 12 + 0
6 + -3k = 12

Add '-6' to each side of the equation.
6 + -6 + -3k = 12 + -6

Combine like terms: 6 + -6 = 0
0 + -3k = 12 + -6
-3k = 12 + -6

Combine like terms: 12 + -6 = 6
-3k = 6

Divide each side by '-3'.
k = -2

Simplifying
k = -2