-2k^2-k+12=3k^2+6k

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Solution for -2k^2-k+12=3k^2+6k equation: 


Simplifying
-2k2 + -1k + 12 = 3k2 + 6k

Reorder the terms:
12 + -1k + -2k2 = 3k2 + 6k

Reorder the terms:
12 + -1k + -2k2 = 6k + 3k2

Solving
12 + -1k + -2k2 = 6k + 3k2

Solving for variable 'k'.

Reorder the terms:
12 + -1k + -6k + -2k2 + -3k2 = 6k + 3k2 + -6k + -3k2

Combine like terms: -1k + -6k = -7k
12 + -7k + -2k2 + -3k2 = 6k + 3k2 + -6k + -3k2

Combine like terms: -2k2 + -3k2 = -5k2
12 + -7k + -5k2 = 6k + 3k2 + -6k + -3k2

Reorder the terms:
12 + -7k + -5k2 = 6k + -6k + 3k2 + -3k2

Combine like terms: 6k + -6k = 0
12 + -7k + -5k2 = 0 + 3k2 + -3k2
12 + -7k + -5k2 = 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
12 + -7k + -5k2 = 0

Factor a trinomial.
(1 + -1k)(12 + 5k) = 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 '(12 + 5k)' equal to zero and attempt to solve:

Simplifying
12 + 5k = 0

Solving
12 + 5k = 0

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

Add '-12' to each side of the equation.
12 + -12 + 5k = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 5k = 0 + -12
5k = 0 + -12

Combine like terms: 0 + -12 = -12
5k = -12

Divide each side by '5'.
k = -2.4

Simplifying
k = -2.4
Solution
k = {1, -2.4}

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