(k-2)(k+5)=18

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Solution for (k-2)(k+5)=18 equation: 


Simplifying
(k + -2)(k + 5) = 18

Reorder the terms:
(-2 + k)(k + 5) = 18

Reorder the terms:
(-2 + k)(5 + k) = 18

Multiply (-2 + k) * (5 + k)
(-2(5 + k) + k(5 + k)) = 18
((5 * -2 + k * -2) + k(5 + k)) = 18
((-10 + -2k) + k(5 + k)) = 18
(-10 + -2k + (5 * k + k * k)) = 18
(-10 + -2k + (5k + k2)) = 18

Combine like terms: -2k + 5k = 3k
(-10 + 3k + k2) = 18

Solving
-10 + 3k + k2 = 18

Solving for variable 'k'.

Reorder the terms:
-10 + -18 + 3k + k2 = 18 + -18

Combine like terms: -10 + -18 = -28
-28 + 3k + k2 = 18 + -18

Combine like terms: 18 + -18 = 0
-28 + 3k + k2 = 0

Factor a trinomial.
(-7 + -1k)(4 + -1k) = 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 '(4 + -1k)' equal to zero and attempt to solve:

Simplifying
4 + -1k = 0

Solving
4 + -1k = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1k = 0 + -4

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

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

Divide each side by '-1'.
k = 4

Simplifying
k = 4
Solution
k = {-7, 4}

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