k(k+5)=2(k+20)

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Solution for k(k+5)=2(k+20) equation: 


Simplifying
k(k + 5) = 2(k + 20)

Reorder the terms:
k(5 + k) = 2(k + 20)
(5 * k + k * k) = 2(k + 20)
(5k + k2) = 2(k + 20)

Reorder the terms:
5k + k2 = 2(20 + k)
5k + k2 = (20 * 2 + k * 2)
5k + k2 = (40 + 2k)

Solving
5k + k2 = 40 + 2k

Solving for variable 'k'.

Reorder the terms:
-40 + 5k + -2k + k2 = 40 + 2k + -40 + -2k

Combine like terms: 5k + -2k = 3k
-40 + 3k + k2 = 40 + 2k + -40 + -2k

Reorder the terms:
-40 + 3k + k2 = 40 + -40 + 2k + -2k

Combine like terms: 40 + -40 = 0
-40 + 3k + k2 = 0 + 2k + -2k
-40 + 3k + k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
-40 + 3k + k2 = 0

Factor a trinomial.
(-8 + -1k)(5 + -1k) = 0


Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve:

Simplifying
-8 + -1k = 0

Solving
-8 + -1k = 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 + -1k = 0 + 8

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

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

Divide each side by '-1'.
k = -8

Simplifying
k = -8

Subproblem 2
Set the factor '(5 + -1k)' equal to zero and attempt to solve:

Simplifying
5 + -1k = 0

Solving
5 + -1k = 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 + -1k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1k = 0 + -5
-1k = 0 + -5

Combine like terms: 0 + -5 = -5
-1k = -5

Divide each side by '-1'.
k = 5

Simplifying
k = 5
Solution
k = {-8, 5}

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