2[x+(x+2)+(x+4)]=(x+2)(x+4)-5

Solution for 2[x+(x+2)+(x+4)]=(x+2)(x+4)-5 equation:

Simplifying
2[x + (x + 2) + (x + 4)] = (x + 2)(x + 4) + -5

Reorder the terms:
2[x + (2 + x) + (x + 4)] = (x + 2)(x + 4) + -5

Remove parenthesis around (2 + x)
2[x + 2 + x + (x + 4)] = (x + 2)(x + 4) + -5

Reorder the terms:
2[x + 2 + x + (4 + x)] = (x + 2)(x + 4) + -5

Remove parenthesis around (4 + x)
2[x + 2 + x + 4 + x] = (x + 2)(x + 4) + -5

Reorder the terms:
2[2 + 4 + x + x + x] = (x + 2)(x + 4) + -5

Combine like terms: 2 + 4 = 6
2[6 + x + x + x] = (x + 2)(x + 4) + -5

Combine like terms: x + x = 2x
2[6 + 2x + x] = (x + 2)(x + 4) + -5

Combine like terms: 2x + x = 3x
2[6 + 3x] = (x + 2)(x + 4) + -5
[6 * 2 + 3x * 2] = (x + 2)(x + 4) + -5
[12 + 6x] = (x + 2)(x + 4) + -5

Reorder the terms:
12 + 6x = (2 + x)(x + 4) + -5

Reorder the terms:
12 + 6x = (2 + x)(4 + x) + -5

Multiply (2 + x) * (4 + x)
12 + 6x = (2(4 + x) + x(4 + x)) + -5
12 + 6x = ((4 * 2 + x * 2) + x(4 + x)) + -5
12 + 6x = ((8 + 2x) + x(4 + x)) + -5
12 + 6x = (8 + 2x + (4 * x + x * x)) + -5
12 + 6x = (8 + 2x + (4x + x2)) + -5

Combine like terms: 2x + 4x = 6x
12 + 6x = (8 + 6x + x2) + -5

Reorder the terms:
12 + 6x = 8 + -5 + 6x + x2

Combine like terms: 8 + -5 = 3
12 + 6x = 3 + 6x + x2

Add '-6x' to each side of the equation.
12 + 6x + -6x = 3 + 6x + -6x + x2

Combine like terms: 6x + -6x = 0
12 + 0 = 3 + 6x + -6x + x2
12 = 3 + 6x + -6x + x2

Combine like terms: 6x + -6x = 0
12 = 3 + 0 + x2
12 = 3 + x2

Solving
12 = 3 + x2

Solving for variable 'x'.

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

Add '-1x2' to each side of the equation.
12 + -1x2 = 3 + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
12 + -1x2 = 3 + 0
12 + -1x2 = 3

Add '-12' to each side of the equation.
12 + -12 + -1x2 = 3 + -12

Combine like terms: 12 + -12 = 0
0 + -1x2 = 3 + -12
-1x2 = 3 + -12

Combine like terms: 3 + -12 = -9
-1x2 = -9

Divide each side by '-1'.
x2 = 9

Simplifying
x2 = 9

Take the square root of each side:
x = {-3, 3}