7k^2+41k-56=0

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Solution for 7k^2+41k-56=0 equation: 


Simplifying
7k2 + 41k + -56 = 0

Reorder the terms:
-56 + 41k + 7k2 = 0

Solving
-56 + 41k + 7k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -1k)(8 + -7k) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(8 + -7k)' equal to zero and attempt to solve:

Simplifying
8 + -7k = 0

Solving
8 + -7k = 0

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

Add '-8' to each side of the equation.
8 + -8 + -7k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -7k = 0 + -8
-7k = 0 + -8

Combine like terms: 0 + -8 = -8
-7k = -8

Divide each side by '-7'.
k = 1.142857143

Simplifying
k = 1.142857143
Solution
k = {-7, 1.142857143}

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