2k^2+9k=-7

Solution for 2k^2+9k=-7 equation:

Simplifying
2k2 + 9k = -7

Reorder the terms:
9k + 2k2 = -7

Solving
9k + 2k2 = -7

Solving for variable 'k'.

Reorder the terms:
7 + 9k + 2k2 = -7 + 7

Combine like terms: -7 + 7 = 0
7 + 9k + 2k2 = 0

Factor a trinomial.
(7 + 2k)(1 + k) = 0

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

Simplifying
1 + k = 0

Solving
1 + k = 0

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

Add '-1' to each side of the equation.
1 + -1 + k = 0 + -1

Combine like terms: 1 + -1 = 0
0 + k = 0 + -1
k = 0 + -1

Combine like terms: 0 + -1 = -1
k = -1

Simplifying
k = -1
Solution
k = {-3.5, -1}