2(2+x)(x+2)=800

Solution for 2(2+x)(x+2)=800 equation:

Simplifying
2(2 + x)(x + 2) = 800

Reorder the terms:
2(2 + x)(2 + x) = 800

Multiply (2 + x) * (2 + x)
2(2(2 + x) + x(2 + x)) = 800
2((2 * 2 + x * 2) + x(2 + x)) = 800
2((4 + 2x) + x(2 + x)) = 800
2(4 + 2x + (2 * x + x * x)) = 800
2(4 + 2x + (2x + x2)) = 800

Combine like terms: 2x + 2x = 4x
2(4 + 4x + x2) = 800
(4 * 2 + 4x * 2 + x2 * 2) = 800
(8 + 8x + 2x2) = 800

Solving
8 + 8x + 2x2 = 800

Solving for variable 'x'.

Reorder the terms:
8 + -800 + 8x + 2x2 = 800 + -800

Combine like terms: 8 + -800 = -792
-792 + 8x + 2x2 = 800 + -800

Combine like terms: 800 + -800 = 0
-792 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-396 + 4x + x2) = 0

Factor a trinomial.
2((-22 + -1x)(18 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-22 + -1x)' equal to zero and attempt to solve:

Simplifying
-22 + -1x = 0

Solving
-22 + -1x = 0

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

Add '22' to each side of the equation.
-22 + 22 + -1x = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -1x = 0 + 22
-1x = 0 + 22

Combine like terms: 0 + 22 = 22
-1x = 22

Divide each side by '-1'.
x = -22

Simplifying
x = -22
Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve:

Simplifying
18 + -1x = 0

Solving
18 + -1x = 0

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

Add '-18' to each side of the equation.
18 + -18 + -1x = 0 + -18

Combine like terms: 18 + -18 = 0
0 + -1x = 0 + -18
-1x = 0 + -18

Combine like terms: 0 + -18 = -18
-1x = -18

Divide each side by '-1'.
x = 18

Simplifying
x = 18
Solution
x = {-22, 18}