(k-7)(k+2)=0

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Solution for (k-7)(k+2)=0 equation: 


Simplifying
(k + -7)(k + 2) = 0

Reorder the terms:
(-7 + k)(k + 2) = 0

Reorder the terms:
(-7 + k)(2 + k) = 0

Multiply (-7 + k) * (2 + k)
(-7(2 + k) + k(2 + k)) = 0
((2 * -7 + k * -7) + k(2 + k)) = 0
((-14 + -7k) + k(2 + k)) = 0
(-14 + -7k + (2 * k + k * k)) = 0
(-14 + -7k + (2k + k2)) = 0

Combine like terms: -7k + 2k = -5k
(-14 + -5k + k2) = 0

Solving
-14 + -5k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-2 + -1k)(7 + -1k) = 0


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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2

Subproblem 2
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
Solution
k = {-2, 7}

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