(5k+10)(6k+7)=0

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Solution for (5k+10)(6k+7)=0 equation: 


Simplifying
(5k + 10)(6k + 7) = 0

Reorder the terms:
(10 + 5k)(6k + 7) = 0

Reorder the terms:
(10 + 5k)(7 + 6k) = 0

Multiply (10 + 5k) * (7 + 6k)
(10(7 + 6k) + 5k * (7 + 6k)) = 0
((7 * 10 + 6k * 10) + 5k * (7 + 6k)) = 0
((70 + 60k) + 5k * (7 + 6k)) = 0
(70 + 60k + (7 * 5k + 6k * 5k)) = 0
(70 + 60k + (35k + 30k2)) = 0

Combine like terms: 60k + 35k = 95k
(70 + 95k + 30k2) = 0

Solving
70 + 95k + 30k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '5'.
5(14 + 19k + 6k2) = 0

Factor a trinomial.
5((2 + k)(7 + 6k)) = 0

Ignore the factor 5.

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

Simplifying
2 + k = 0

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

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

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

Simplifying
k = -2

Subproblem 2
Set the factor '(7 + 6k)' equal to zero and attempt to solve:

Simplifying
7 + 6k = 0

Solving
7 + 6k = 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 + 6k = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6k = 0 + -7
6k = 0 + -7

Combine like terms: 0 + -7 = -7
6k = -7

Divide each side by '6'.
k = -1.166666667

Simplifying
k = -1.166666667
Solution
k = {-2, -1.166666667}

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