4k^2+18k+21=3

Solution for 4k^2+18k+21=3 equation:

Simplifying
4k2 + 18k + 21 = 3

Reorder the terms:
21 + 18k + 4k2 = 3

Solving
21 + 18k + 4k2 = 3

Solving for variable 'k'.

Reorder the terms:
21 + -3 + 18k + 4k2 = 3 + -3

Combine like terms: 21 + -3 = 18
18 + 18k + 4k2 = 3 + -3

Combine like terms: 3 + -3 = 0
18 + 18k + 4k2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(9 + 9k + 2k2) = 0

Factor a trinomial.
2((3 + k)(3 + 2k)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + k)' equal to zero and attempt to solve:

Simplifying
3 + k = 0

Solving
3 + k = 0

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

Add '-3' to each side of the equation.
3 + -3 + k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + k = 0 + -3
k = 0 + -3

Combine like terms: 0 + -3 = -3
k = -3

Simplifying
k = -3
Subproblem 2
Set the factor '(3 + 2k)' equal to zero and attempt to solve:

Simplifying
3 + 2k = 0

Solving
3 + 2k = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2k = 0 + -3
2k = 0 + -3

Combine like terms: 0 + -3 = -3
2k = -3

Divide each side by '2'.
k = -1.5

Simplifying
k = -1.5
Solution
k = {-3, -1.5}