(3k-8)(k+7)=0

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Solution for (3k-8)(k+7)=0 equation: 


Simplifying
(3k + -8)(k + 7) = 0

Reorder the terms:
(-8 + 3k)(k + 7) = 0

Reorder the terms:
(-8 + 3k)(7 + k) = 0

Multiply (-8 + 3k) * (7 + k)
(-8(7 + k) + 3k * (7 + k)) = 0
((7 * -8 + k * -8) + 3k * (7 + k)) = 0
((-56 + -8k) + 3k * (7 + k)) = 0
(-56 + -8k + (7 * 3k + k * 3k)) = 0
(-56 + -8k + (21k + 3k2)) = 0

Combine like terms: -8k + 21k = 13k
(-56 + 13k + 3k2) = 0

Solving
-56 + 13k + 3k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -1k)(8 + -3k) = 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 '(8 + -3k)' equal to zero and attempt to solve:

Simplifying
8 + -3k = 0

Solving
8 + -3k = 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 + -3k = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3k = 0 + -8
-3k = 0 + -8

Combine like terms: 0 + -8 = -8
-3k = -8

Divide each side by '-3'.
k = 2.666666667

Simplifying
k = 2.666666667
Solution
k = {-7, 2.666666667}

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