(2)(2+2x+6)=(x)(x+x)

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

Simplifying
(2)(2 + 2x + 6) = (x)(x + x)

Reorder the terms:
2(2 + 6 + 2x) = (x)(x + x)

Combine like terms: 2 + 6 = 8
2(8 + 2x) = (x)(x + x)
(8 * 2 + 2x * 2) = (x)(x + x)
(16 + 4x) = (x)(x + x)

Combine like terms: x + x = 2x
16 + 4x = x(2x)

Remove parenthesis around (2x)
16 + 4x = x * 2x

Reorder the terms for easier multiplication:
16 + 4x = 2x * x

Multiply x * x
16 + 4x = 2x2

Solving
16 + 4x = 2x2

Solving for variable 'x'.

Combine like terms: 2x2 + -2x2 = 0
16 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(8 + 2x + -1x2) = 0

Factor a trinomial.
2((4 + -1x)(2 + x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Solution
x = {4, -2}