3(4k^2+34k+70)=0

Solution for 3(4k^2+34k+70)=0 equation:

Simplifying
3(4k2 + 34k + 70) = 0

Reorder the terms:
3(70 + 34k + 4k2) = 0
(70 * 3 + 34k * 3 + 4k2 * 3) = 0
(210 + 102k + 12k2) = 0

Solving
210 + 102k + 12k2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '6'.
6(35 + 17k + 2k2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(5 + k)' equal to zero and attempt to solve:

Simplifying
5 + k = 0

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

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

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

Simplifying
k = -5
Subproblem 2
Set the factor '(7 + 2k)' equal to zero and attempt to solve:

Simplifying
7 + 2k = 0

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

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

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

Divide each side by '2'.
k = -3.5

Simplifying
k = -3.5
Solution
k = {-5, -3.5}