-k^2-13k+49=8k-3k^2

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Solution for -k^2-13k+49=8k-3k^2 equation: 


Simplifying
-1k2 + -13k + 49 = 8k + -3k2

Reorder the terms:
49 + -13k + -1k2 = 8k + -3k2

Solving
49 + -13k + -1k2 = 8k + -3k2

Solving for variable 'k'.

Reorder the terms:
49 + -13k + -8k + -1k2 + 3k2 = 8k + -3k2 + -8k + 3k2

Combine like terms: -13k + -8k = -21k
49 + -21k + -1k2 + 3k2 = 8k + -3k2 + -8k + 3k2

Combine like terms: -1k2 + 3k2 = 2k2
49 + -21k + 2k2 = 8k + -3k2 + -8k + 3k2

Reorder the terms:
49 + -21k + 2k2 = 8k + -8k + -3k2 + 3k2

Combine like terms: 8k + -8k = 0
49 + -21k + 2k2 = 0 + -3k2 + 3k2
49 + -21k + 2k2 = -3k2 + 3k2

Combine like terms: -3k2 + 3k2 = 0
49 + -21k + 2k2 = 0

Factor a trinomial.
(7 + -2k)(7 + -1k) = 0


Subproblem 1
Set the factor '(7 + -2k)' equal to zero and attempt to solve:

Simplifying
7 + -2k = 0

Solving
7 + -2k = 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 + -2k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2k = 0 + -7
-2k = 0 + -7

Combine like terms: 0 + -7 = -7
-2k = -7

Divide each side by '-2'.
k = 3.5

Simplifying
k = 3.5

Subproblem 2
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
Solution
k = {3.5, 7}

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