-7k(7k-1)-3(-7k-7)=1+5k-6k

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Solution for -7k(7k-1)-3(-7k-7)=1+5k-6k equation: 


Simplifying
-7k(7k + -1) + -3(-7k + -7) = 1 + 5k + -6k

Reorder the terms:
-7k(-1 + 7k) + -3(-7k + -7) = 1 + 5k + -6k
(-1 * -7k + 7k * -7k) + -3(-7k + -7) = 1 + 5k + -6k
(7k + -49k2) + -3(-7k + -7) = 1 + 5k + -6k

Reorder the terms:
7k + -49k2 + -3(-7 + -7k) = 1 + 5k + -6k
7k + -49k2 + (-7 * -3 + -7k * -3) = 1 + 5k + -6k
7k + -49k2 + (21 + 21k) = 1 + 5k + -6k

Reorder the terms:
21 + 7k + 21k + -49k2 = 1 + 5k + -6k

Combine like terms: 7k + 21k = 28k
21 + 28k + -49k2 = 1 + 5k + -6k

Combine like terms: 5k + -6k = -1k
21 + 28k + -49k2 = 1 + -1k

Solving
21 + 28k + -49k2 = 1 + -1k

Solving for variable 'k'.

Reorder the terms:
21 + -1 + 28k + k + -49k2 = 1 + -1k + -1 + k

Combine like terms: 21 + -1 = 20
20 + 28k + k + -49k2 = 1 + -1k + -1 + k

Combine like terms: 28k + k = 29k
20 + 29k + -49k2 = 1 + -1k + -1 + k

Reorder the terms:
20 + 29k + -49k2 = 1 + -1 + -1k + k

Combine like terms: 1 + -1 = 0
20 + 29k + -49k2 = 0 + -1k + k
20 + 29k + -49k2 = -1k + k

Combine like terms: -1k + k = 0
20 + 29k + -49k2 = 0

Factor a trinomial.
(1 + -1k)(20 + 49k) = 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 '(20 + 49k)' equal to zero and attempt to solve:

Simplifying
20 + 49k = 0

Solving
20 + 49k = 0

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

Add '-20' to each side of the equation.
20 + -20 + 49k = 0 + -20

Combine like terms: 20 + -20 = 0
0 + 49k = 0 + -20
49k = 0 + -20

Combine like terms: 0 + -20 = -20
49k = -20

Divide each side by '49'.
k = -0.4081632653

Simplifying
k = -0.4081632653
Solution
k = {1, -0.4081632653}

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