x[4x+14]=-6

Solution for x[4x+14]=-6 equation:

Simplifying
x[4x + 14] = -6

Reorder the terms:
x[14 + 4x] = -6
[14 * x + 4x * x] = -6
[14x + 4x2] = -6

Solving
14x + 4x2 = -6

Solving for variable 'x'.

Reorder the terms:
6 + 14x + 4x2 = -6 + 6

Combine like terms: -6 + 6 = 0
6 + 14x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 7x + 2x2) = 0

Factor a trinomial.
2((3 + x)(1 + 2x)) = 0

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

Simplifying
x = -3
Subproblem 2
Set the factor '(1 + 2x)' equal to zero and attempt to solve:

Simplifying
1 + 2x = 0

Solving
1 + 2x = 0

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

Add '-1' to each side of the equation.
1 + -1 + 2x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2x = 0 + -1
2x = 0 + -1

Combine like terms: 0 + -1 = -1
2x = -1

Divide each side by '2'.
x = -0.5

Simplifying
x = -0.5
Solution
x = {-3, -0.5}