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

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


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

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

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

Multiply (-2 + K) * (7 + K)
(-2(7 + K) + K(7 + K)) = 0
((7 * -2 + K * -2) + K(7 + K)) = 0
((-14 + -2K) + K(7 + K)) = 0
(-14 + -2K + (7 * K + K * K)) = 0
(-14 + -2K + (7K + K2)) = 0

Combine like terms: -2K + 7K = 5K
(-14 + 5K + K2) = 0

Solving
-14 + 5K + K2 = 0

Solving for variable 'K'.

Factor a trinomial.
(-7 + -1K)(2 + -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 '(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
Solution
K = {-7, 2}

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