49k^2=-294-385k

Solution for 49k^2=-294-385k equation:

Simplifying
49k2 = -294 + -385k

Solving
49k2 = -294 + -385k

Solving for variable 'k'.

Reorder the terms:
294 + 385k + 49k2 = -294 + -385k + 294 + 385k

Reorder the terms:
294 + 385k + 49k2 = -294 + 294 + -385k + 385k

Combine like terms: -294 + 294 = 0
294 + 385k + 49k2 = 0 + -385k + 385k
294 + 385k + 49k2 = -385k + 385k

Combine like terms: -385k + 385k = 0
294 + 385k + 49k2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(42 + 55k + 7k2) = 0

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

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

Simplifying
7 + k = 0

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

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

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

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

Simplifying
6 + 7k = 0

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

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

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

Divide each side by '7'.
k = -0.8571428571

Simplifying
k = -0.8571428571
Solution
k = {-7, -0.8571428571}