-7k^2+7k-40=2+8k-8k^2

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Solution for -7k^2+7k-40=2+8k-8k^2 equation: 


Simplifying
-7k2 + 7k + -40 = 2 + 8k + -8k2

Reorder the terms:
-40 + 7k + -7k2 = 2 + 8k + -8k2

Solving
-40 + 7k + -7k2 = 2 + 8k + -8k2

Solving for variable 'k'.

Reorder the terms:
-40 + -2 + 7k + -8k + -7k2 + 8k2 = 2 + 8k + -8k2 + -2 + -8k + 8k2

Combine like terms: -40 + -2 = -42
-42 + 7k + -8k + -7k2 + 8k2 = 2 + 8k + -8k2 + -2 + -8k + 8k2

Combine like terms: 7k + -8k = -1k
-42 + -1k + -7k2 + 8k2 = 2 + 8k + -8k2 + -2 + -8k + 8k2

Combine like terms: -7k2 + 8k2 = 1k2
-42 + -1k + 1k2 = 2 + 8k + -8k2 + -2 + -8k + 8k2

Reorder the terms:
-42 + -1k + 1k2 = 2 + -2 + 8k + -8k + -8k2 + 8k2

Combine like terms: 2 + -2 = 0
-42 + -1k + 1k2 = 0 + 8k + -8k + -8k2 + 8k2
-42 + -1k + 1k2 = 8k + -8k + -8k2 + 8k2

Combine like terms: 8k + -8k = 0
-42 + -1k + 1k2 = 0 + -8k2 + 8k2
-42 + -1k + 1k2 = -8k2 + 8k2

Combine like terms: -8k2 + 8k2 = 0
-42 + -1k + 1k2 = 0

Factor a trinomial.
(-6 + -1k)(7 + -1k) = 0


Subproblem 1
Set the factor '(-6 + -1k)' equal to zero and attempt to solve:

Simplifying
-6 + -1k = 0

Solving
-6 + -1k = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1k = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1k = 0 + 6
-1k = 0 + 6

Combine like terms: 0 + 6 = 6
-1k = 6

Divide each side by '-1'.
k = -6

Simplifying
k = -6

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 = {-6, 7}

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