7(k-5)(k+1)=0

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Solution for 7(k-5)(k+1)=0 equation: 


Simplifying
7(k + -5)(k + 1) = 0

Reorder the terms:
7(-5 + k)(k + 1) = 0

Reorder the terms:
7(-5 + k)(1 + k) = 0

Multiply (-5 + k) * (1 + k)
7(-5(1 + k) + k(1 + k)) = 0
7((1 * -5 + k * -5) + k(1 + k)) = 0
7((-5 + -5k) + k(1 + k)) = 0
7(-5 + -5k + (1 * k + k * k)) = 0
7(-5 + -5k + (1k + k2)) = 0

Combine like terms: -5k + 1k = -4k
7(-5 + -4k + k2) = 0
(-5 * 7 + -4k * 7 + k2 * 7) = 0
(-35 + -28k + 7k2) = 0

Solving
-35 + -28k + 7k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-5 + -4k + k2) = 0

Factor a trinomial.
7((-1 + -1k)(5 + -1k)) = 0

Ignore the factor 7.

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

Simplifying
-1 + -1k = 0

Solving
-1 + -1k = 0

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

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

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

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

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

Simplifying
k = -1

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 = {-1, 5}

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