6k^2-14k-52=-7k-3

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Solution for 6k^2-14k-52=-7k-3 equation: 


Simplifying
6k2 + -14k + -52 = -7k + -3

Reorder the terms:
-52 + -14k + 6k2 = -7k + -3

Reorder the terms:
-52 + -14k + 6k2 = -3 + -7k

Solving
-52 + -14k + 6k2 = -3 + -7k

Solving for variable 'k'.

Reorder the terms:
-52 + 3 + -14k + 7k + 6k2 = -3 + -7k + 3 + 7k

Combine like terms: -52 + 3 = -49
-49 + -14k + 7k + 6k2 = -3 + -7k + 3 + 7k

Combine like terms: -14k + 7k = -7k
-49 + -7k + 6k2 = -3 + -7k + 3 + 7k

Reorder the terms:
-49 + -7k + 6k2 = -3 + 3 + -7k + 7k

Combine like terms: -3 + 3 = 0
-49 + -7k + 6k2 = 0 + -7k + 7k
-49 + -7k + 6k2 = -7k + 7k

Combine like terms: -7k + 7k = 0
-49 + -7k + 6k2 = 0

Factor a trinomial.
(-7 + -3k)(7 + -2k) = 0


Subproblem 1
Set the factor '(-7 + -3k)' equal to zero and attempt to solve:

Simplifying
-7 + -3k = 0

Solving
-7 + -3k = 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 + -3k = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -3k = 0 + 7
-3k = 0 + 7

Combine like terms: 0 + 7 = 7
-3k = 7

Divide each side by '-3'.
k = -2.333333333

Simplifying
k = -2.333333333

Subproblem 2
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
Solution
k = {-2.333333333, 3.5}

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