5(3k-5)(7k+2)=0

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Solution for 5(3k-5)(7k+2)=0 equation: 


Simplifying
5(3k + -5)(7k + 2) = 0

Reorder the terms:
5(-5 + 3k)(7k + 2) = 0

Reorder the terms:
5(-5 + 3k)(2 + 7k) = 0

Multiply (-5 + 3k) * (2 + 7k)
5(-5(2 + 7k) + 3k * (2 + 7k)) = 0
5((2 * -5 + 7k * -5) + 3k * (2 + 7k)) = 0
5((-10 + -35k) + 3k * (2 + 7k)) = 0
5(-10 + -35k + (2 * 3k + 7k * 3k)) = 0
5(-10 + -35k + (6k + 21k2)) = 0

Combine like terms: -35k + 6k = -29k
5(-10 + -29k + 21k2) = 0
(-10 * 5 + -29k * 5 + 21k2 * 5) = 0
(-50 + -145k + 105k2) = 0

Solving
-50 + -145k + 105k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-10 + -29k + 21k2) = 0

Factor a trinomial.
5((-2 + -7k)(5 + -3k)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(-2 + -7k)' equal to zero and attempt to solve:

Simplifying
-2 + -7k = 0

Solving
-2 + -7k = 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 + -7k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -7k = 0 + 2
-7k = 0 + 2

Combine like terms: 0 + 2 = 2
-7k = 2

Divide each side by '-7'.
k = -0.2857142857

Simplifying
k = -0.2857142857

Subproblem 2
Set the factor '(5 + -3k)' equal to zero and attempt to solve:

Simplifying
5 + -3k = 0

Solving
5 + -3k = 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 + -3k = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -3k = 0 + -5
-3k = 0 + -5

Combine like terms: 0 + -5 = -5
-3k = -5

Divide each side by '-3'.
k = 1.666666667

Simplifying
k = 1.666666667
Solution
k = {-0.2857142857, 1.666666667}

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