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

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


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

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

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

Reorder the terms:
-63k + -7k2 = -45k + -14k + 9k2

Combine like terms: -45k + -14k = -59k
-63k + -7k2 = -59k + 9k2

Solving
-63k + -7k2 = -59k + 9k2

Solving for variable 'k'.

Reorder the terms:
-63k + 59k + -7k2 + -9k2 = -59k + 9k2 + 59k + -9k2

Combine like terms: -63k + 59k = -4k
-4k + -7k2 + -9k2 = -59k + 9k2 + 59k + -9k2

Combine like terms: -7k2 + -9k2 = -16k2
-4k + -16k2 = -59k + 9k2 + 59k + -9k2

Reorder the terms:
-4k + -16k2 = -59k + 59k + 9k2 + -9k2

Combine like terms: -59k + 59k = 0
-4k + -16k2 = 0 + 9k2 + -9k2
-4k + -16k2 = 9k2 + -9k2

Combine like terms: 9k2 + -9k2 = 0
-4k + -16k2 = 0

Factor out the Greatest Common Factor (GCF), '-4k'.
-4k(1 + 4k) = 0

Ignore the factor -4.

Subproblem 1
Set the factor 'k' equal to zero and attempt to solve:

Simplifying
k = 0

Solving
k = 0

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

Simplifying
k = 0

Subproblem 2
Set the factor '(1 + 4k)' equal to zero and attempt to solve:

Simplifying
1 + 4k = 0

Solving
1 + 4k = 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 + 4k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4k = 0 + -1
4k = 0 + -1

Combine like terms: 0 + -1 = -1
4k = -1

Divide each side by '4'.
k = -0.25

Simplifying
k = -0.25
Solution
k = {0, -0.25}

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