-7k(k+9)=9(k-5)-14k

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Solution for -7k(k+9)=9(k-5)-14k equation: 


Simplifying
-7k(k + 9) = 9(k + -5) + -14k

Reorder the terms:
-7k(9 + k) = 9(k + -5) + -14k
(9 * -7k + k * -7k) = 9(k + -5) + -14k
(-63k + -7k2) = 9(k + -5) + -14k

Reorder the terms:
-63k + -7k2 = 9(-5 + k) + -14k
-63k + -7k2 = (-5 * 9 + k * 9) + -14k
-63k + -7k2 = (-45 + 9k) + -14k

Combine like terms: 9k + -14k = -5k
-63k + -7k2 = -45 + -5k

Solving
-63k + -7k2 = -45 + -5k

Solving for variable 'k'.

Reorder the terms:
45 + -63k + 5k + -7k2 = -45 + -5k + 45 + 5k

Combine like terms: -63k + 5k = -58k
45 + -58k + -7k2 = -45 + -5k + 45 + 5k

Reorder the terms:
45 + -58k + -7k2 = -45 + 45 + -5k + 5k

Combine like terms: -45 + 45 = 0
45 + -58k + -7k2 = 0 + -5k + 5k
45 + -58k + -7k2 = -5k + 5k

Combine like terms: -5k + 5k = 0
45 + -58k + -7k2 = 0

Factor a trinomial.
(5 + -7k)(9 + k) = 0


Subproblem 1
Set the factor '(5 + -7k)' equal to zero and attempt to solve:

Simplifying
5 + -7k = 0

Solving
5 + -7k = 0

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

Add '-5' to each side of the equation.
5 + -5 + -7k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -7k = 0 + -5
-7k = 0 + -5

Combine like terms: 0 + -5 = -5
-7k = -5

Divide each side by '-7'.
k = 0.7142857143

Simplifying
k = 0.7142857143

Subproblem 2
Set the factor '(9 + k)' equal to zero and attempt to solve:

Simplifying
9 + k = 0

Solving
9 + k = 0

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

Add '-9' to each side of the equation.
9 + -9 + k = 0 + -9

Combine like terms: 9 + -9 = 0
0 + k = 0 + -9
k = 0 + -9

Combine like terms: 0 + -9 = -9
k = -9

Simplifying
k = -9
Solution
k = {0.7142857143, -9}

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