21k^2+5k+5=-6k+7

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Solution for 21k^2+5k+5=-6k+7 equation:


Simplifying
21k2 + 5k + 5 = -6k + 7

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

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

Solving
5 + 5k + 21k2 = 7 + -6k

Solving for variable 'k'.

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

Combine like terms: 5 + -7 = -2
-2 + 5k + 6k + 21k2 = 7 + -6k + -7 + 6k

Combine like terms: 5k + 6k = 11k
-2 + 11k + 21k2 = 7 + -6k + -7 + 6k

Reorder the terms:
-2 + 11k + 21k2 = 7 + -7 + -6k + 6k

Combine like terms: 7 + -7 = 0
-2 + 11k + 21k2 = 0 + -6k + 6k
-2 + 11k + 21k2 = -6k + 6k

Combine like terms: -6k + 6k = 0
-2 + 11k + 21k2 = 0

Factor a trinomial.
(-2 + -3k)(1 + -7k) = 0


Subproblem 1
Set the factor '(-2 + -3k)' equal to zero and attempt to solve:

Simplifying
-2 + -3k = 0

Solving
-2 + -3k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -3k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -3k = 0 + 2
-3k = 0 + 2

Combine like terms: 0 + 2 = 2
-3k = 2

Divide each side by '-3'.
k = -0.6666666667

Simplifying
k = -0.6666666667

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

Simplifying
1 + -7k = 0

Solving
1 + -7k = 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 + -7k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -7k = 0 + -1
-7k = 0 + -1

Combine like terms: 0 + -1 = -1
-7k = -1

Divide each side by '-7'.
k = 0.1428571429

Simplifying
k = 0.1428571429
Solution
k = {-0.6666666667, 0.1428571429}

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