4k^2+12k+42=-7k+2k^2

Solution for 4k^2+12k+42=-7k+2k^2 equation:

Simplifying
4k2 + 12k + 42 = -7k + 2k2

Reorder the terms:
42 + 12k + 4k2 = -7k + 2k2

Solving
42 + 12k + 4k2 = -7k + 2k2

Solving for variable 'k'.

Reorder the terms:
42 + 12k + 7k + 4k2 + -2k2 = -7k + 2k2 + 7k + -2k2

Combine like terms: 12k + 7k = 19k
42 + 19k + 4k2 + -2k2 = -7k + 2k2 + 7k + -2k2

Combine like terms: 4k2 + -2k2 = 2k2
42 + 19k + 2k2 = -7k + 2k2 + 7k + -2k2

Reorder the terms:
42 + 19k + 2k2 = -7k + 7k + 2k2 + -2k2

Combine like terms: -7k + 7k = 0
42 + 19k + 2k2 = 0 + 2k2 + -2k2
42 + 19k + 2k2 = 2k2 + -2k2

Combine like terms: 2k2 + -2k2 = 0
42 + 19k + 2k2 = 0

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

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

Simplifying
6 + k = 0

Solving
6 + k = 0

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

Add '-6' to each side of the equation.
6 + -6 + k = 0 + -6

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

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

Simplifying
k = -6
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 = {-6, -3.5}