-2k^2-17k+12=8-5k^2-4k

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Solution for -2k^2-17k+12=8-5k^2-4k equation: 


Simplifying
-2k2 + -17k + 12 = 8 + -5k2 + -4k

Reorder the terms:
12 + -17k + -2k2 = 8 + -5k2 + -4k

Reorder the terms:
12 + -17k + -2k2 = 8 + -4k + -5k2

Solving
12 + -17k + -2k2 = 8 + -4k + -5k2

Solving for variable 'k'.

Reorder the terms:
12 + -8 + -17k + 4k + -2k2 + 5k2 = 8 + -4k + -5k2 + -8 + 4k + 5k2

Combine like terms: 12 + -8 = 4
4 + -17k + 4k + -2k2 + 5k2 = 8 + -4k + -5k2 + -8 + 4k + 5k2

Combine like terms: -17k + 4k = -13k
4 + -13k + -2k2 + 5k2 = 8 + -4k + -5k2 + -8 + 4k + 5k2

Combine like terms: -2k2 + 5k2 = 3k2
4 + -13k + 3k2 = 8 + -4k + -5k2 + -8 + 4k + 5k2

Reorder the terms:
4 + -13k + 3k2 = 8 + -8 + -4k + 4k + -5k2 + 5k2

Combine like terms: 8 + -8 = 0
4 + -13k + 3k2 = 0 + -4k + 4k + -5k2 + 5k2
4 + -13k + 3k2 = -4k + 4k + -5k2 + 5k2

Combine like terms: -4k + 4k = 0
4 + -13k + 3k2 = 0 + -5k2 + 5k2
4 + -13k + 3k2 = -5k2 + 5k2

Combine like terms: -5k2 + 5k2 = 0
4 + -13k + 3k2 = 0

Factor a trinomial.
(1 + -3k)(4 + -1k) = 0


Subproblem 1
Set the factor '(1 + -3k)' equal to zero and attempt to solve:

Simplifying
1 + -3k = 0

Solving
1 + -3k = 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 + -3k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3k = 0 + -1
-3k = 0 + -1

Combine like terms: 0 + -1 = -1
-3k = -1

Divide each side by '-3'.
k = 0.3333333333

Simplifying
k = 0.3333333333

Subproblem 2
Set the factor '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1k = 0 + -4
-1k = 0 + -4

Combine like terms: 0 + -4 = -4
-1k = -4

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {0.3333333333, 4}

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