7x(x^2+2x+6)=

Solution for 7x(x^2+2x+6)= equation:

Simplifying
7x(x2 + 2x + 6) = 0

Reorder the terms:
7x(6 + 2x + x2) = 0
(6 * 7x + 2x * 7x + x2 * 7x) = 0
(42x + 14x2 + 7x3) = 0

Solving
42x + 14x2 + 7x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '7x'.
7x(6 + 2x + x2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(6 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 2x + x2 = 0

Solving
6 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 2x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 2x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 2x + x2 = 0 + -6
2x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
2x + x2 = -6

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = -6 + 1

Reorder the terms:
1 + 2x + x2 = -6 + 1

Combine like terms: -6 + 1 = -5
1 + 2x + x2 = -5

Factor a perfect square on the left side:
(x + 1)(x + 1) = -5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}