k^2+5k+6=(k+2)(k+12)

Solution for k^2+5k+6=(k+2)(k+12) equation:

Simplifying
k2 + 5k + 6 = (k + 2)(k + 12)

Reorder the terms:
6 + 5k + k2 = (k + 2)(k + 12)

Reorder the terms:
6 + 5k + k2 = (2 + k)(k + 12)

Reorder the terms:
6 + 5k + k2 = (2 + k)(12 + k)

Multiply (2 + k) * (12 + k)
6 + 5k + k2 = (2(12 + k) + k(12 + k))
6 + 5k + k2 = ((12 * 2 + k * 2) + k(12 + k))
6 + 5k + k2 = ((24 + 2k) + k(12 + k))
6 + 5k + k2 = (24 + 2k + (12 * k + k * k))
6 + 5k + k2 = (24 + 2k + (12k + k2))

Combine like terms: 2k + 12k = 14k
6 + 5k + k2 = (24 + 14k + k2)

Add '-1k2' to each side of the equation.
6 + 5k + k2 + -1k2 = 24 + 14k + k2 + -1k2

Combine like terms: k2 + -1k2 = 0
6 + 5k + 0 = 24 + 14k + k2 + -1k2
6 + 5k = 24 + 14k + k2 + -1k2

Combine like terms: k2 + -1k2 = 0
6 + 5k = 24 + 14k + 0
6 + 5k = 24 + 14k

Solving
6 + 5k = 24 + 14k

Solving for variable 'k'.

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

Add '-14k' to each side of the equation.
6 + 5k + -14k = 24 + 14k + -14k

Combine like terms: 5k + -14k = -9k
6 + -9k = 24 + 14k + -14k

Combine like terms: 14k + -14k = 0
6 + -9k = 24 + 0
6 + -9k = 24

Add '-6' to each side of the equation.
6 + -6 + -9k = 24 + -6

Combine like terms: 6 + -6 = 0
0 + -9k = 24 + -6
-9k = 24 + -6

Combine like terms: 24 + -6 = 18
-9k = 18

Divide each side by '-9'.
k = -2

Simplifying
k = -2