(2x+4)(x+2)=32

Solution for (2x+4)(x+2)=32 equation:

Simplifying
(2x + 4)(x + 2) = 32

Reorder the terms:
(4 + 2x)(x + 2) = 32

Reorder the terms:
(4 + 2x)(2 + x) = 32

Multiply (4 + 2x) * (2 + x)
(4(2 + x) + 2x * (2 + x)) = 32
((2 * 4 + x * 4) + 2x * (2 + x)) = 32
((8 + 4x) + 2x * (2 + x)) = 32
(8 + 4x + (2 * 2x + x * 2x)) = 32
(8 + 4x + (4x + 2x2)) = 32

Combine like terms: 4x + 4x = 8x
(8 + 8x + 2x2) = 32

Solving
8 + 8x + 2x2 = 32

Solving for variable 'x'.

Reorder the terms:
8 + -32 + 8x + 2x2 = 32 + -32

Combine like terms: 8 + -32 = -24
-24 + 8x + 2x2 = 32 + -32

Combine like terms: 32 + -32 = 0
-24 + 8x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-12 + 4x + x2) = 0

Factor a trinomial.
2((-6 + -1x)(2 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6
Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

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

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

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-6, 2}