2k^2+4k+12=10

Solution for 2k^2+4k+12=10 equation:

Simplifying
2k2 + 4k + 12 = 10

Reorder the terms:
12 + 4k + 2k2 = 10

Solving
12 + 4k + 2k2 = 10

Solving for variable 'k'.

Reorder the terms:
12 + -10 + 4k + 2k2 = 10 + -10

Combine like terms: 12 + -10 = 2
2 + 4k + 2k2 = 10 + -10

Combine like terms: 10 + -10 = 0
2 + 4k + 2k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 2k + k2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {-1, -1}